zip -r foo.zip [directory] unzip foo.zip
tar -cvf foo.tar [directory] tar -xvf foo.tar
tar -zcvf foo.tar.gz [directory] tar -zxvf foo.tar.gz tar -zxvf foo.tar.gz -C [directory]
tar -jcvf foo.tar.bz2 [directory] tar -xvjpf foo.tar.bz2
On seeing this error:
.htaccess: Invalid command 'RewriteEngine'
This indicates that rewrite module is not enabled. In Apache 2, both module and sites are handled in the separated folders under /etc/apache2:
mods-available/ mods-enabled/ sites-available/ sites-enabled/
In the *-available folders are the configurations to be used, for instance, here we need to enable rewrite module, we just type
sudo a2enmod rewrite
You see that rewrite.load is in the folder mods-available with the content:
LoadModule rewrite_module /usr/lib/apache2/modules/mod_rewrite.so
You will be notified to restart/reload the Apache service. Do it.
We write the configurations as foo.com in sites/available:
<VirtualHost 127.0.0.3:80>
ServerAdmin webmaster@example.com
ServerName localhost
ServerAlias foo.com
# Indexes + Directory Root.
DirectoryIndex index.php
DocumentRoot /var/www/foo
# Logfiles
ErrorLog /var/www/foo/logs/error.log
CustomLog /var/www/foo/logs/access.log combined
</VirtualHost>
Make sure there is a logs folder
cd /var/www/foo mkdir logs
And then enable the website
sudo a2ensite foo.com
Just to notice how to disable the website:
sudo a2dissite foo.com
Most importantly, enact the changes.
sudo service apache2 restart
This article only talks about PHP installed alongside Apache under Linux (see here). Since PHP is run through libapache2-mod-php5. it inherits the permissions from Apache. So let's take a look about Apache. By default, it uses www-data user, to check this,
ps -u www-data
If it is so, you might get something similar:
PID TTY TIME CMD 1276 ? 00:00:00 php5-fpm 1277 ? 00:00:00 php5-fpm 1278 ? 00:00:00 php5-fpm 1279 ? 00:00:00 php5-fpm 14934 ? 00:00:00 apache2 14935 ? 00:00:00 apache2 14936 ? 00:00:00 apache2 ...
Now check user info and its group of www-data
cat /etc/passwd | grep www-data
The following shows up on my machine which says it doesn't belong to the root group or my administrator group.
www-data:x:33:33:www-data:/var/www:/bin/sh
We list the file permissions of the folder img/ to see apache's right:
ls -l | grep img
All right! Since Apache is in other group here, it doesn't have 'w' permission.
drwxrwxr-x 2 admin admin 4096 Nov 12 19:26 img
Then let's give him the permission. Notice that it is dangerous to do this, since in this way every user on the computer will have rights on this folder. Normally, we let the owner of the folder be Apache, and others can only read.
chmod o+w img
La Terminologia principale del MS Windows in correspondenza fra italiano e inglese. The correspondence of MS Windows terminology between Italian and English.
| account utente | User account |
| aggiornamento | update |
| arresta il sistema | shut down |
| attendere | wait |
| attivazione o disattivazione | activation or disactivation |
| avviare | start |
| barre degli strumenti | Tool bar |
| caricamento | loading |
| cerca | search |
| collegamenti | shortcuts |
| connessioni di rete | Network connection |
| Disinstalla o modifica programma | Uninstall or modify programs |
| disinstalla | uninstall |
| eseguire | execute |
| gestione attività | Task manager |
| Gestione dispositivi | Device Manager |
| ibernazione | hibernate |
| Immagini | Pictures |
| impostazioni | configuration |
| indrizzi | address |
| manutenzione | maintainance |
| Modalità provvisoria | Safe Mode |
| mostra desktop | show desktop |
| nuova | new |
| Pannello di controllo | Control Panel |
| proprietà | property |
| riavvia il sistema | restart |
| risoluzione problemi | Troubleshooting |
| Sistema e sicurezza | System and Security |
| souni | sound |
| stampante | printer |
| strumento | tool |
To sort a random file by alphabet,
sort -gk 2 temp
Don't force it, there must be a screw under.
One screwdriver undoes all the screws, what a design!
Most overheating problems are caused by an untidy fan.
click to enlarge
Rename the extensions of all files,
for FILE in *.foo ; do NEWFILE=`echo $FILE | sed 's/.foo/.bar/g'` ; mv "$FILE" $NEWFILE ; done
Test if a variable is set (pay attention to the space, they can't be eliminated),
if [ ! -z "$var" ]; then echo "var exists" fi
Test if a file exists,
if [ -f "$file" ]; then echo "file exists" fi
Copy one file to the clipboard (install xclip first)
cat file | xclip -selection c
Paste clipboard to a file
xclip -o > file
Define a function
foo(){
echo "FUNCTION"
}
fun=$(foo)
The most recent foreground pipeline exit status: $?
if [ $? -eq -1 ] then exit 1 fi
Several ways of for loop controlled by a var
for I in {1..10}; do echo $I; done
for I in 1 2 3 4 5 6 7 8 9 10; do echo $I; done
for I in $(seq 1 10); do echo $I; done
for ((I=1; I <= 10 ; I++)); do echo $I; done
Generate ticks in (-4pi, 4pi):
for i in $(seq -4 4); do b=`echo "$i * 3.14159" | bc`; echo -ne $b","; done;
This is useful for PGFplots for trigonometric ticks,
xtick={-12.56636,-9.42477,-6.28318,-3.14159,0,
3.14159,6.28318,9.42477,12.56636},
xticklabels={
$-4\pi$, $-3\pi$, $-2\pi$, $-\pi$, $0$,
$\pi$, $2\pi$, $3\pi$, $4\pi$
}
Convert all jpeg files and save them as png files.
for file in *.jpg;do newfile=`echo $file | sed 's/.jpg/.png/g'`; gm convert -quality 60 $file $newfile; done
Compress all jpeg files.
mkdir new for file in *.jpg;do newfile="new/$file"; gm convert -quality 60 $file $newfile; done
This list of knowledge is a collection of common problems encountered in everyday typesetting. The solution is either seen by reading package manuals of LaTeX related websites. But here I would like to give a list of clear reference (let's do it in factory mode). I've evaluated different solutions and try to make the hacks as simple as possible.
By default, hyperref packages creates a colorful border for links. To remove it,
%remove colorful borders on links without updating the package
\hypersetup{%
pdfborder = {0 0 0}
}
How to use "List of Algorithms" as toc title and "Algorithms" for single title instead of "List of Listings" while using listings package?
%listing customization
\renewcommand{\lstlistingname}{Algorithm}% Listing -> Algorithm
\renewcommand{\lstlistlistingname}{List of \lstlistingname s}% List of Listings -> List of Algorithms
How not to break hypen in bibliography?
%bibliography no break hypen
\makeatletter
\newcommand*\bibhyphen{\hbox{-}\nobreak\hskip\z@skip}
\makeatother
\newcommand*\bibdash{\rule[0.48ex]{2em}{0.14ex}\space}
How to add bibliography to the table of contents?
\usepackage[nottoc]{tocbibind} %add bibliography to toc
How to use "bibliography" instead of "references"?
\renewcommand{\refname}{Bibliography}
How to enlarge margin paragraph width without using geometry package since it rewrites all the default layout values?
%set twice as default
\setlength{\marginparwidth}{2\marginparwidth}
How to center texts?
%maybe you are looking for \vspace{2cm} too?
\begin{center}
This is centered text.
\end{center}
How to give remarks in red?
\usepackage{color}
%you can define a macro \remark in the preamble
\newcommand{\remark}[1]{{\color{red}REMARK: #1}}
%then in the document
\remark{This is a remark in red.}
To include Chinese/Japanese/Korean letters or characters along with pdflatex, use CJK package. Alternatively, one can choose xelatex. See CJK Doc. Notice CJK env uses two extra options to specify the encodings and font family. One can check out supported font family by checking the folder /usr/share/texmf/tex/latex/CJK/UTF8 or similar. If the font parameter is empty, the default value given in CJK.enc will be selected. On my machine, I have c70bkai.fd installed in that folder. One can also refer install CJK support to see how to manually install a CJK font to the tex tree.
\usepackage{CJK}
\begin{CJK}{UTF8}{bkai}
漢字
\end{CJK}
%to merge CJK with another environment, embed that environment within CJK, such as
\begin{CJK}{UTF8}{bkai}
\marginpar{
丁香
}
\end{CJK}
An example of including a centered figure with caption and label.
\usepackage{grahpicx}
\begin{figure}[ht]
\centering
\includegraphics{pic.jpg}
\caption{sample picture}
\label{fig:sample-pic}
\end{figure}
How to put two pictures side by side with each of its own caption and label?
\usepackage{subfigure}
\begin{figure}[ht]
\centering
\subfigure[Caption a]{
\includegraphics[width=.45\linewidth]{img1.png}
\label{fig:imga}
}
\hspace{.2in}
\subfigure[Caption b]{
\includegraphics[width=.45\linewidth]{img2.png}
\label{fig:imgb}
}
\caption{Two figures}%
\label{fig:2-fig}
\end{figure}
How to introduce plain codes?
\usepackage{verbatim}
\begin{verbatim}
int sched_setscheduler(pid_t pid, int policy,
const struct sched_param *param);
\end{verbatim}
How to include "Acknowledgements"?
%do it as a section
\section*{Acknowledgements}
\addcontentsline{toc}{section}{Acknowledgements}
Customize figure caption. This caption will remove "Fig.", and the separator is set as space instead of the default colon.
\renewcommand{\figurename}{}
\usepackage[labelsep=space]{caption}
Symbols: (U)p (B)ack (L)eft (R)ight (F)ront, U' means rotating in counter-clockwise direction, while U means clockwise.
Problem: Skype icon not showing on panel tray (top bar) and launcher (left bar)
Affected: Ubuntu 12.04
Cause: installation from .deb
Solution:
sudo apt-get install sni-qt sni-qt:i386 gsettings get com.canonical.Unity.Panel systray-whitelist gsettings set com.canonical.Unity.Panel systray-whitelist "['JavaEmbeddedFrame', 'Wine', 'Update-notifier', 'Skype']"
Source:
How do I Get the Skype Status Icon Back on Panel TrayNote: This guide is for Linux.
/usr/lib/scicoslab-gtk-4.4.1/), usesudo cp -r scipad/* /usr/lib/scicoslab-gtk-4.4.1/
The lesson here is that mv command doesn't have -r option, so cp is all right.
sudo scicoslab
genlib("utillib");
Exit and restart scicoslab, and that will be okay.
--> v = zeros(1:20)
To launch the embedded editor, type
--> scipad
One can write a sequence of Scicos instructions and save it as *.sci files. To load such a program into ScicosLab, type
--> exec('foo.sci');
It inherits a Linux style,
--> pwd --> ls --> cd
To clear terminal screen, use either one
--> ctrl+l --> clc
For instance,
function [re,im] = compute(v, f)
re=re+cos(2*%pi*f*v/1000000);
im=im+sin(2*%pi*f*v/1000000);
return [re,im];
endfunction
The return value is a vector [re,im], as you might notice, the Scicos language is C-like but not strong-typed. This function compute takes two params. Notice that the incremental sum is not supported, that is re+=... commits an error. Once loaded into ScicosLab, it works as library functions. You can call it anytime, but after a clear command, it vanishes as all the other customized variables do.
for i=1:20, printf("%d\n",i); end
Notice that no increment of i is needed. It does so automatically at every loop.
i=1;
while i<=20, printf("%d\n",i);i++; end
TBD.
Fourier's building blocks were sine and cosine waves. All the majesty of periodic functions can be constructed by them.
Just a glimpse. A periodic function $f(x)$, with $(-\pi, \pi)$ as its basic periodic unit, can be approached by the sum of an infinite series.
$$a_0 = \frac{1}{2\pi} \int_{-\pi}^{\pi} f(x)dx \\ a_n = \frac{1}{\pi} \int_{-\pi}^{\pi} f(x)\cos(nx)dx \\ b_n = \frac{1}{\pi} \int_{-\pi}^{\pi} f(x)\sin(nx)dx \\ a_0 + \sum_{n=1}^{\infty}(a_n \cos (nx) + b_n \sin (nx))$$
Also a quick glance,
$$\mathcal{F}(f(t))(s) = \int_{-\infty}^{+\infty} f(t)e^{-2\pi i s t} dt$$
A bit into the point. The input of DFT is a finite series of equally-spaced (in time) samples. e.g., f(0), f(0.1), f(0.2), ..., f(2π), and the output is a series of complex numbers encoding the amplitude and phase information, say $\mathcal{F}(0)$, $\mathcal{F}(F_0)$, ..., $\mathcal{F}(-F_0)$. And $F_0$ is the fundamental frequency, which is calculated as
$$F_0 = \frac{1}{N \Delta}$$$\Delta$ is the sample period, in our example it is $0.1$. The x-axis of these numbers are the frequency spaced as in the figure below,
However, the discrete transform is thus performed, $$\mathcal{F}(n) = \sum_{k=0}^{N} f(k) e^{-2\pi i n k/N}$$
The basic calculation unit is a vector or a matrix in ScicosLab. What we get used to is a 1*1 matrix.
--> 0:0.1:4*%pi
Well, the result is stored in the variable ans and the vector will be displayed hereafter. This vector is comprised of float numbers from 0 to 4π with a spacing of 0.1, they are 116 numbers, check this with the function length(). Yes, %pi is the Scicos way of pre-defining some constants. For the logarithmic natural base e, it uses %e. To stop printing results after each command, one can end it with a semi-colon(;).
--> a = 0:0.1:4*%pi;
Variables are type-free when being declared, so the initialization will make the variable a being a vector. Any assignment will change its content and type just like using a brand-new variable. The system preserved variable ans will be updated in the same fashion after executing every command.
--> a = sin(a);
--> plot(a);
This gives you a sine wave of 2 periods.
--> v = dft(a,-1); --> clf(); --> plot(v);
To check the usage of a function or related entries, use
--> apropos fourier --> help dft
To clear the graph/figure, use the function clf(). We see in the new plotting
ScicosLab just drew the real part of frequency components, to compare with the imaginary parts, use
--> plot(imag(v), 'red');
The figure gets re-shaped and we see two spikes again. As a matter of fact, the Fourier transform of sine wave is two dirac functions.
--> browsevar --> clear
The former gives a window of currently being-used variables, and the latter command just destroys them.
The data file temp is lines of float numbers with one at each line.
--> fp = mopen("temp","r");
--> v = mfscanf(-1,fp,"%f");
--> v';
In principle, dash application icons are located under /usr/share/icons/hicolor/apps, however, this can be customized. For instance, the configuration for a program named ScicosLab lies in /usr/share/applications/scicoslab.desktop, it has the following content:
[Desktop Entry]
Name=ScicosLab
Comment=Scientific Computing using ScicosLab
TryExec=/usr/bin/scicoslab
Exec=/usr/bin/scicoslab
Icon=/usr/lib/scicoslab-gtk-4.4.1/config/puffin-gtk48.png
Terminal=false
Type=Application
Categories=Education;Science;Math;
StartupNotify=false
X-Desktop-File-Install-Version=0.15
One can restart the system to see the effect.
sudo gtk-update-icon-cache --force /usr/share/icons/hicolor
Boolean formulas are represented in diagrams. OBDD has the following property, $$\phi \leftrightarrow \psi \Rightarrow OBDD(\phi) = OBDD(\psi)$$
$\xi : S \rightarrow $boolean formulas (OBDDs). By definition, $$\xi([\phi]) := \xi(\{ s | M,s \models \phi \})$$
A list of some symbolic encodings,
The above exactly parallels the classical fixed-points techniques. See a previous post (link).
The following shows the symbolic counterpart for the classical fixed points algorithms (denotational, based on states). Recall their inductive version,
OBDD PreImage(OBDD X){
return ∃V'. (X[V'] ∧ ξ(R)[V,V']);
}
OBDD Check_EG(OBDD X) {
Y′ := X;
repeat
Y := Y′;
Y′ := Y ∧ PreImage(Y);
until (Y′ ↔ Y);
return Y;
}
OBDD Check_EU(OBDD X1 ,X2) {
Y′ := X2;
repeat
Y := Y′;
Y′ := Y ∨ (X1 ∧ PreImage(Y));
until (Y′ ↔ Y);
return Y;
}
Here we need to refer Emerson Lei algorithm which specifies the fair CTL version. $$ [\mathbf{E}_f \mathbf{G} \phi ] = \nu Z .([\phi] \cap \bigcap_{F_i \in FT} [\mathbf{EX}[\mathbf{E}(Z \mathbf{U}(Z \wedge F_i ))])$$
The can be interpreted as $Z$ keeps being true until all fair conditions are met when $Z$ is still true at each step of iteration.
OBDD Check_FairEG(OBDD X) {
Z’ := X;
repeat
Z := Z’;
for each Fi in FT
Y := Check_EU(Z, Fi ∧ Z);
Z’:= Z’ ∧ PreImage(Y);
end for;
until (Z’ ↔ Z);
return Z;
}
Invariants are specified as $\mathbf{AG}\phi$. Its negation is $\neg \mathbf{EF} \neg \phi$, which is a reachability issue: are there such states which can be reached from the initial states? We show the forward checking technique.
OBDD Compute_reachable() {
Y′ := I;
Y := ⊥;
while ¬(Y′ ↔ Y) {
Y := Y′;
Y′ := Y ∨ Image(Y);
}
return Y;
}
Note backward checking iteratively calculates the preimage of $\phi$ until a fixed-point is reached or the preimage intersects with $I$. An advanced version with the so-called frontier (F) is presented below.
OBDD Compute_reachable() {
Y := I;
F := I;
while ¬(F ↔ ⊥) {
F := Image(F) ∧ ¬Y;
Y := F ∨ Y;
}
return Y;
}
If we explain it in the set flavor, it could be at each time we only calculate the image of new states (frontier). The set of reachable states is saturated when the image of the frontier can't bring in more new states.
Based on the discussion above, we now can check invariants (often feature as bad behaviors).
bool Forward_Check_EF(OBDD BAD) {
Y := F := I;
while ¬(F ↔ ⊥) and (F ∧ BAD) ↔ ⊥ {
F := Image(F ) ∧ ¬Y ;
Y := Y ∨ F ;
}
if F = ⊥
return false
else
return true
}
The above utilizes the frontier technique. It looks for all reachable states and verifies whether there are some bad states within them.
The most of this post is heavily extracted from the RS's teaching slides, hence I don't claim the copyright. The character of this post is intended to be a note, with marginal and personal remarks. For those who need to respect the source, please read the following copy of the original copyright notice.
Copyright notice: some material (text, figures) displayed in these slides is courtesy of M. Benerecetti, A. Cimatti, P. Pandya, M. Pistore, M. Roveri, and S.Tonetta, who detain its copyright. Some exampes displayed in these slides are taken from [Clarke, Grunberg & Peled, “Model Checking”, MIT Press], and their copyright is detained by the authors. All the other material is copyrighted by Roberto Sebastiani. Every commercial use of this material is strictly forbidden by the copyright laws without the authorization of the authors. No copy of these slides can be displayed in public without containing this copyright notice.
Complete lattice is a partially-ordered set which has join ($\cup$) and meet ($\cap$) operators. The former generates the least lower bound and the latter the greatest upper bound. The state space of a Kripke model forms a complete lattice under containment, i.e. $(2^S, \subseteq)$ is a complete lattice.
$F$ is monotonic if $\forall a < b$, $F(a) < F(b)$.
A monotonic function over a complete lattice has the least and the greatest fixed point.
The mentioned fixed points can be calculated this way. Assume $F$ is a monotonic function and $\cup$-continuous (increments), the least fixed point must be reached (this chain converges): $$\emptyset \subseteq F(\emptyset) \subseteq F(F(\emptyset)) \subseteq \ldots$$
Instead, if $F$ is $\cap$-continuous (decrements), the greatest fixed point is obtained by, $$S \supseteq F(S) \supseteq F(F(S)) \supseteq \ldots$$
All CTL formulae can be rewritten in terms of $\neg, \wedge, \mathbf{EX}, \mathbf{EU}, \mathbf{EG}$ only.
Although irrelevant at this context, but it is worthy to note that $\mathbf{EG}\phi = \mathbf{E}(\bot \mathbf{R} \phi)$, this is to say $\phi$ is never released (has to be true forever).
In CTL model checking, the calculating unit is a set of states that satisfy some formula $\phi$, noted as denotation $[\phi]$. Pre-Image maps the image (in the range) back to the domain (its pre-image). It is thus defined, $$\mathsf{PreImage}([\phi]) = \{s | \exists (s, s') \in R \wedge s' \in [\phi]\}$$
$\mathsf{PreImage}$ is a monotonic function over the complete lattice $(2^S, \subseteq)$, thus Kleene's theorem applies. Pre-Image matches the idea of $\mathbf{EX}$, i.e. $[\mathbf{EX}\phi]$ is the pre-image of $[\phi]$.
According to tableaux rules, $\mathbf{EG}$, $\mathbf{EF}$, $\mathbf{EU}$s are written in the form of fixed points ($\nu$: greatest, $\mu$: least.).
So given a CTL formula $\phi$, after rewriting, we apply the set operations for negations (complement the set) and disjunctions (union), and fixed points for temporal formulas. We say $M \models \phi$ iff $I \subseteq [\phi]$.
The previous post introduced the declarative construction, which is exponential. For instance, the LGBA for $p \mathbf{U} q$ has 8 states. However, on-the-fly construction can build Büchi automata for linear size. Surely, distinct automata can express the same language (further, the LTL formula).
First we write LTL formulas into their NNF equivalence, which is composed by $\vee, \wedge, \mathbf{X}, \mathbf{U}, \mathbf{R}$ only. Negations are pushed down to literals. Here we quote some rules,
With all formulas converted to the following form, each disjunct is a state.
$$\bigvee_i \bigg( \bigwedge_j I_{ij} \wedge \bigwedge_k \mathbf{X}\psi_{ik} \bigg)$$Note $\bigwedge_j I_{ij}$ represents the labels, and $\bigwedge_k \mathbf{X}\psi_{ik}$ shows the transition. When the $\mathbf{X}$-formula is not present, we write $\mathbf{X} \top$.
A cover of a set of LTL formulas $\Psi= \{ \psi_1, \ldots, \psi_k \}$ calculates the set of initial states of Büchi automaton that represents $\bigwedge_i \psi_i$. A state is denoted as $\langle \lambda, \chi, \sigma \rangle$, which are the set of labels, the next formula, the set of subformulas of satisfied in $s$.
$$\mathsf{Cover}(\Psi) := \mathsf{Expand}(\Psi, \langle \emptyset, \emptyset, \emptyset \rangle)$$We quote its definition. Assume $s=\langle \lambda, \chi, \sigma \rangle$, $l$ is a propositional literal, $\mathsf{Expand}(\Psi, s)=$
\begin{align*} \begin{cases} s & \Psi = \emptyset \\ \emptyset & \bot \in \Psi \\ \mathsf{Expand}(\Psi \backslash \top , s) & \top \in \Psi \\ \mathsf{Expand}(\Psi \backslash \{l\}, \langle \lambda \cup \{l\}, \chi, \sigma \cup \{l\} \rangle) & l \in \Psi \\ \mathsf{Expand}(\Psi \backslash \{\mathbf{X}\psi\}, \langle \lambda , \chi \cup \{ \psi \}, \sigma \cup \{\mathbf{X}\psi\} \rangle) & \mathbf{X}\psi \in \Psi \\ \mathsf{Expand}(\Psi \cup \{\psi_1, \psi_2\} \backslash \{\psi_1 \wedge \psi_2\}, \\ \quad \quad \quad \langle \lambda, \chi, \sigma \cup \{\psi_1 \wedge \psi_2\} \rangle) & \psi_1 \wedge \psi_2 \in \Psi \\ \mathsf{Expand}(\Psi \cup \{\psi_1\} \backslash \{\psi_1 \vee \psi_2\}, \\ \quad \quad \quad \langle \lambda, \chi, \sigma \cup \{\psi_1 \vee \psi_2\} \rangle) \cup \\ \mathsf{Expand}(\Psi \cup \{\psi_2\} \backslash \{\psi_1 \vee \psi_2\}, \\ \quad \quad \quad \langle \lambda, \chi, \sigma \cup \{\psi_1 \vee \psi_2\} \rangle) & \psi_1 \vee \psi_2 \in \Psi \\ \mathsf{Expand}(\Psi \cup \{\psi_1\} \backslash \{\psi_1 \mathbf{U} \psi_2\}, \\ \quad \quad \quad \langle \lambda, \chi \cup \{\psi_1 \mathbf{U} \psi_2\}, \sigma \cup \{\psi_1 \mathbf{U} \psi_2\} \rangle) \cup \\ \mathsf{Expand}(\Psi \cup \{\psi_2\} \backslash \{\psi_1 \mathbf{U} \psi_2\}, \\ \quad \quad \quad \langle \lambda, \chi, \sigma \cup \{\psi_1 \mathbf{U} \psi_2\} \rangle) & \psi_1 \mathbf{U} \psi_2 \in \Psi \\ \mathsf{Expand}(\Psi \cup \{\psi_2\} \backslash \{\psi_1 \mathbf{R} \psi_2\}, \\ \quad \quad \quad \langle \lambda, \chi \cup \{\psi_1 \mathbf{R} \psi_2\}, \sigma \cup \{\psi_1 \mathbf{U} \psi_2\} \rangle) \cup \\ \mathsf{Expand}(\Psi \cup \{\psi_1, \psi_2\} \backslash \{\psi_1 \mathbf{R} \psi_2\}, \\ \quad \quad \quad \langle \lambda, \chi, \sigma \cup \{\psi_1 \mathbf{R} \psi_2\} \rangle) & \psi_1 \mathbf{R} \psi_2 \in \Psi \end{cases} \end{align*}With the above operations defined, we construct the Büchi Automaton for an LTL formula. $A_\phi = (Q, Q_0 , \Sigma, L, T , FT)$, with $Q_0 = \mathsf{Cover}(\{\phi\})$, $Q$ is the smallest set such that $Q_0 \subseteq Q$, also if $\langle \lambda, \chi, \sigma \rangle \in Q$, then $\mathsf{Cover}(\{\chi\}) \in Q$, the labeling function $L(s) = \{a \in \Sigma | a \models \lambda \}$, transition relation $T = \{(s,s') | s = \langle \lambda, \chi, \sigma \rangle \wedge s' \in \mathsf{Cover}(\{\chi\}) \}$, the fairness conditions $FT = \{F_1, \ldots, F_n\}$, where $F_i = \{s \in Q | \phi_i \mathbf{U} \psi_i \notin \sigma \vee \psi_i \in \sigma \}$.
Here we present the Büchi Automata built from the stated method.
Fig 1. NBA of $\mathbf{FG}p$
Fig 2. NBA of $p \mathbf{U} q$
The following is a copy of original copyright notice of slides which this article is quoting.
Copyright notice: some material (text, figures) displayed in these slides is courtesy of M. Benerecetti, A. Cimatti, P. Pandya, M. Pistore, M. Roveri, and S.Tonetta, who detain its copyright. Some exampes displayed in these slides are taken from [Clarke, Grunberg & Peled, “Model Checking”, MIT Press], and their copyright is detained by the authors. All the other material is copyrighted by Roberto Sebastiani. Every commercial use of this material is strictly forbidden by the copyright laws without the authorization of the authors. No copy of these slides can be displayed in public without containing this copyright notice.
LTL formulae are translated in Labelled Generalized Büchi Automata (LGBA), where labels are moved into states. See a previous post (link).
An $\omega$-automaton is an automaton which accepts infinite inputs. Büchi Automata are a typical example. An $\omega$-word is an accepting run on an $\omega$-automaton, the set of all $\omega$-words accepted (defined) by an $\omega$-automaton is called an $\omega$-language.
The alphabet of a language is denoted as $\Sigma$, the set of all $\omega$-words composed by symbols in $\Sigma$ is denoted as $\Sigma^{\omega}$. A language recognizable (accepted) by an automaton $A$ is written $L(A)$. Usually we only work in automata that have $L(A) \subset \Sigma^{\omega}$.
Recall that regular languages can be recognized by NFAs/DFAs (equivalent). It can also be generated by regular grammar (left linear or right linear, but not mixed).
A language is called $\omega$-regular when it is represented as $$\bigcup_{i=1}^n U_i(V_i)^{\omega}$$
we require that $U_i$, $V_i$ be regular languages. $L$ is $\omega$-regular iff it can be recognized by Nondeterministic Büchi Automata. The $\omega$-regular languages are closed under complementation (useful for constructing $A_{\neg\phi}$).
The closure of an LTL formula is intended to calculate its components (including their negations). For instance, a closure set of $p\mathbf{U}q$ is $$\{p, q, p\mathbf{U}q, \mathbf{X}(p\mathbf{U}q), \neg p, \neg q, \neg (p\mathbf{U}q), \neg (\mathbf{X}(p\mathbf{U}q))\}$$
An atom $A$ is called a maximal consistent subset of the closure set. First we remove negations. In order to be consistent (agree on assignments), we should have $p,q \in A$ when we have $p \wedge q \in A$. Similarly, when we have $p\mathbf{U}q \in A$, we require either $q \in A$ or $\{p \in A, \mathbf{X}(p\mathbf{U}q)\} \subset A$.
$A_{\phi} = (Q, Q_0, \Sigma, L, T, FT)$, respectively, the set of states Q is the the set of all atoms of $\phi$, the set of initial states $Q_0$ are the atoms where $\phi$ is included, $\Sigma$ is the power set of all free variables in $\phi$, namely the alphabet, labeling function $L$ maps a state to the set of free variables appeared in that state, transition relation is built from $\mathbf{X}$-formulas, say $(\mathbf{X}\psi, \psi) \in T$, $FT$ is a set of fair conditions $\{F_1, \ldots, F_n \}$, where $$F_i = \{ s \text{ is an atom} | \psi \mathbf{U} \phi \in s \vee \phi \in s \}$$
The above is on the condition that $\psi \mathbf{U} \phi$ appears positively in $\phi$. (see Polarity)
One can calculate the atoms of $p \mathbf{U} q$ and other parameters by the stated method, thus its Büchi automaton.
Fig 1. $A_{p \mathbf{U} q}$ constructed by definition
The above construction is called declarative construction, though an alternative is present, considering its volume, it is to be introduced in another post.
The following is a copy of original copyright notice of slides which this article is quoting.
Copyright notice: some material (text, figures) displayed in these slides is courtesy of M. Benerecetti, A. Cimatti, P. Pandya, M. Pistore, M. Roveri, and S.Tonetta, who detain its copyright. Some exampes displayed in these slides are taken from [Clarke, Grunberg & Peled, “Model Checking”, MIT Press], and their copyright is detained by the authors. All the other material is copyrighted by Roberto Sebastiani. Every commercial use of this material is strictly forbidden by the copyright laws without the authorization of the authors. No copy of these slides can be displayed in public without containing this copyright notice.
Let $M$ be a Kripke model, and $\psi$ be an LTL formula. The model checking problem is whether $$M \models \psi$$
It is rephrased in the manner of Büchi automaton for automatic reasoning. We express both the model and the formula in Büchi automata ($A_M$, $A_\psi$), then the model checking problem is to check whether the language of $A_M$ is contained by the language of $A_\psi$, that is, $\mathcal{L}(A_M) \subseteq \mathcal{L}(A_{\psi})$. In other words, whatever $A_M$ expresses is well captured in $A_\psi$. Further, if we negate $\psi$, then the containment becomes emptiness checking. i.e. $$\mathcal{L}(A_M) \cap \mathcal{L}(A_{\neg\psi}) = \varnothing$$
Unlike NFA/DFAs, Büchi automata have infinite words (aka. $\omega$-words). The "final" states are a set of accepting states, where a loop exists. A run on automata is an infinite execution of automaton, e.g., say the alphabet is $\Sigma = \{a,b\}$, $F=\{b\}$, a legal run can be $\rho = abbbbbb\cdots$.
Like NFA, Non-deterministic Büchi automata (NBA) have transition relations $\delta : Q \rightarrow Q $ as partial ($Q$ is the set of states), while the deterministic one total. But the subset construction from NFA to DFA doesn't apply here.
Given a Kripke model $M$, we add an initial state, and move labels from states to incoming edges, every state becomes an accepting state. The fair version is to change the accepting states only to fair states.
We need to move the labels of Büchi Automata into states. LGBA features a set of fair conditions $FT = \{F_1, ..., F_k \}$, an accepting run must concord with all fair conditions. Formally, $$\forall i . \mathsf{inf}(\rho) \cap F_i \neq \varnothing$$ where $\mathsf{inf}$ calculates the accepting states of the run $\rho$, $F_i \subseteq Q$. Further, an LGBA has a set of initial states rather than only one in BA.
This part is relatively big and it will be introduced in another post.
Compared to synchronous product of NFAs, NBAs' product employs a tag $(1,2)$ specifying on which NBA it is running. The synchronous product is used to calculate the language intersection, $$\mathcal{L}(A_1 \times A_2) = \mathcal{L} (A_1) \cap \mathcal{L} (A_2)$$
Initial state of the product, $I = I_1 \times I_2 \times \{ 1 \}$, accepting states $F = F_1 \times Q_2 \times \{ 1 \}$, transition relations are defined such that a run on track 1 ends at one of its accepting states $F_1$, then moves on to track 2 until meeting some state in $F_2$, then it switches back. The product has such initial states and finite states to ensure that an infinite run of the product automaton must infinitely run on both $A_1$ and $A_2$.
The complementation involves conversion to Rabin automaton. This is to construct $A_{\neg\phi}$.
The problem can be addressed as searching an accepting cycle reachable from an initial state. Double nested DFS algorithm employs two Hash tables, two stacks and two nested DFS routines. The following is routine 1,
DFS1(NBA A) {
stack S1=I; stack S2=∅;
Hashtable T1=I; Hashtable T2=∅;
while (S1!=∅) {
v=top(S1);
if ∃w s.t. w∈ δ(v) && T1(w)==0 {
hash(w,T1);
push(w,S1);
} else {
pop(S1);
if v∈F DFS2(v,S2,T2,A);
}
}
return EMPTY;
}
The following is routine 2,
DFS2(state f, stack S, Hashtable T, NBA A) {
hash(f,T);
push(f,S);
while (S!=∅) {
v=top(S);
if f∈ δ(v) return NOT_EMPTY;
if ∃w s.t. w∈ δ(v) && T(w)==0 {
hash(w);
push(w);
} else pop(S);
}
}
DFS1 starts with the initial state, hashes each state on the path when visiting it for the first time. It invokes DFS2 when no more moves are possible and the top of stack is an accepting state. DFS2 tries to search a loop starting from this accepting state and going back to itself. When such a loop is found, it means $A$ is not empty, and the path is a combination of stack 1 and stack 2.
The following is a copy of original copyright notice of slides which this article is quoting.
Copyright notice: some material (text, figures) displayed in these slides is courtesy of M. Benerecetti, A. Cimatti, P. Pandya, M. Pistore, M. Roveri, and S.Tonetta, who detain its copyright. Some exampes displayed in these slides are taken from [Clarke, Grunberg & Peled, “Model Checking”, MIT Press], and their copyright is detained by the authors. All the other material is copyrighted by Roberto Sebastiani. Every commercial use of this material is strictly forbidden by the copyright laws without the authorization of the authors. No copy of these slides can be displayed in public without containing this copyright notice.
Always read instructions carefully.- #1 note on a survival manual, Yann Martel Life of Pi
On Android, everything is an app.- mzt
Shell for Android is an app too. Install Terminal IDE (210MB) from the app store. Yes, this is not built-in, not default, also with limited use: vi, javac, gcc, git, ssh etc. It runs without root permission. After the installation, switch on its ugly but complete keyboard to get the full function use.
Under Terminal IDE, gcc is paralleled by terminal-gcc, which is not installed by default (due to the volume of gcc). If you go to help file from its main menu, you will see a series of tutorials explaining how to start making the best use of it. Here I just quote the part on gcc. On any of its terminal window (there are 4),
# cat `which install_gcc` # install_gcc
After installation, use the following command to compile,
# terminal-gcc foo.c -o foo.o
See appendix for credits.
Bounded Model Checking (BMC) is a SAT-based technique, distinguished from symbolic model checking. It converts model checking problem into satisfiability problem. BMC tends to look for counter-examples by progressively increasing an integer bound, which is the number of steps in a path. Yes, once you verified there are no counter-examples within the bound $k$, it doesn't prove $M \models f$ at all. BMC is useful in troubleshooting, to capture the flaws in the model design.
Given a Kripke model $M$, a LTL formula $f$ and a bound $k$,
$M \models_k \mathbf{E}f$ iff ⟦$M$,$f$⟧$_k$ is satisfiable.
$\models_k$ means the property is verified in the path of $k$ steps. ⟦$M$,$f$⟧$_k$ is defined as follows,
Fig. 1 The encoding of ⟦$M$,$f$⟧$_k$ in BMC
(1) divides the denotion into the model part (2) and the property part (3). (2) shows the execution of $M$ in $k$ steps, by providing the initial state ($s_0$ is a vector of boolean variables that are assigned in such state) and transition relations of each step. (3) also consists of two portions that disjunct. The first portion says there are no loops at $s_k$ to all former states (negation of transition relation from $s_k$ to $s_{k-1}$,..., $s_0$). The second one is with loops.
Fig. 2 The paths with and without loop
We do need to separate the encodings (i.e. ⟦$f$⟧$^i_k$, $_l$⟦$f$⟧$^i_k$). For instance, only the finite path carrying a loop can verify the properties like $\mathbf{G}p$. We need to describe properties in different manner according to the existence of a loop. Here is the formal chart,
Fig. 3 ⟦$f$⟧$^i_k$ and $_l$⟦$f$⟧$^i_k$ unfolded alongside their LTL correspondence
The above is a recursive definition. The indices $i$, $k$, $l$ say respectively the current state, the integer bound, the loop point (there is an edge from $s_k$ back to $s_l$). The base case $p$, an atom, matches $p_i$ which is the assignment of $p$ at the state $s_i$. The negation is thereby defined. The loop doesn't matter for these two since we only consider an atom in the current state. The disjunction and conjunction are defined recursively. Before going further, we shall see this figure,
Fig. 4 The loop case
$\mathbf{X}g$ parallels a conditional branch definition. In the loop-less case, when $i < k$, the current state is before the bound state, then there is a next state for $s_i$. Otherwise false. Similar in the loop case, but when $i = k$, since there is a loop from $s_k$ to $s_l$, the next state exists. Think there is no $i > k$, when it loops back, $k+1$ becomes $l$, so everything is still within the bound $k$.
$\mathbf{G}g$ is simply false in the loop-less case, always UNSAT. If there is a loop, we need to make sure every state (hence as a big conjunction) with in the loop verifies $g$ and also the relays from the current state $s_i$ to the loop point $s_l$ in case of $i < l$.
$\mathbf{F}g$ is straight-forward, regarding the fact that we'd like at least one $g$ on such path (both loop-less and with loop), so a big disjunction is used.
Recall that $h \mathbf{U} g$ means $h$ remains true till $g$ becomes true. So in the loop-less case, it compares to the disjunction (satisfiable at least one of the components is true) of all possible captures, e.g., $g_i$, $h_ig_{i+1}$, $h_ih_{i+1}g_{i+2}$, ..., etc. Similar for $h \mathbf{R} g$, which says the advent of the truth of $h$ releases $g$ from being always true. That said, $g$ wasn't free (being true always) before $h$ gets its truth.
The situation becomes much more complex in the loop case for these two. If $i < l$, then it gets the part similar to the loop-less one, $$ \bigvee_{j=i}^k \bigg( {}_l\llbracket \; g \; \lrbracket_k^j \wedge \bigwedge_{n=i}^{j-1} {}_l \llbracket \; h \; \lrbracket ^n_k \bigg)$$ It is accompanied by the case that $i > l$, the idea is the property shall be verified from $s_i$ to $s_k$, then from $s_l$ to $s_{i-1}$ since there is loop $(s_k, s_l)$. So we have, $$ \bigvee_{j=l}^{i-1} \bigg( {}_l\llbracket \; g \; \lrbracket_k^j \wedge \bigwedge_{n=i}^{k} {}_l \llbracket \; h \; \lrbracket ^n_k \wedge \bigwedge_{n=l}^{j-1} {}_l\llbracket \; h \; \lrbracket_k^n \bigg)$$
The last one can be accordingly rendered.
The following is a copy of original copyright notice of slides where the images here were taken.
Copyright notice: some material (text, figures) displayed in these slides is courtesy of M. Benerecetti, A. Cimatti, P. Pandya, M. Pistore, M. Roveri, and S.Tonetta, who detain its copyright. Some exampes displayed in these slides are taken from [Clarke, Grunberg & Peled, “Model Checking”, MIT Press], and their copyright is detained by the authors. All the other material is copyrighted by Roberto Sebastiani. Every commercial use of this material is strictly forbidden by the copyright laws without the authorization of the authors. No copy of these slides can be displayed in public without containing this copyright notice.
See appendix for credits.
Conflict-Driven backtracking is a huge advancement to the classical chronological backtracking applied to the DPLL algorithm. It solves the Boolean formulas with about $10^7$ variables.
The idea was to learn from error. When we see a conflict, we find the cause (building a conflict set), and we go back to the decision point where we could do it differently if we have had known this conflict set. It seems hard to catch for a machine. However, it is operable through the following algorithm. This is the most advanced modern approach in many SAT solvers.
Data structure: stack partitioned into decision levels. Each level comprises of a decision literal and its implied literals (unit-propagated). Every implied literal is tagged with the clause causing its unit propagation (aka. antecedent clause).
One level in the stack can be depicted by an implication graph, where there are nodes and edges. A node without edges means a decision literal , because an edge is are marked with the antecedent clause of the literal. E.g.,
Fig. 1 An Implication Graph (Shown on Right)
It has two steps,
1. C := conflicting clause
2. repeat {
C <- resolve C with the antecedent clause of the last
unit-propagated literal in C
}
until { C verifies some termination criteria }
Well, we wonder what this "resolve" mean, it is a disjunction but removing $A_i \vee \neg A_i$ since they become true. Resolution is a rule saying two input clauses entails the output clause (aka. resolvent). For a detailed discussion, see Resolution (logic). By performing this, the unit propagation is undone. What about some termination criteria? Here comes the magic.
It means First Unique Implication Point, this is the state-of-the-art strategy. It is the first point where we find only one literal of current decision level in C. For instance (built from the same example above),
Fig. 2 Conflict set construction
Upon this, we build the conflict set: $\{ \neg A_{10} , \neg A_{11} , A_4 \}$, and "learn" (add) a new clause $c_{10} := A_{10} ∨ A_{11} ∨ \neg A_4$. Now that we reached the conflict, also we know these $\neg A_{10}$, $\neg A_{11}$ can not survive with $A_4$, so we backtrack to $\neg A_{11}$, and right there we assign $\neg A_4$. Yes, we cut off all paths to $A_4$ from that point on. We would never fall into this conflict set again (we learned from the error).
We saved all these learned clauses, on a larger scale ($10^7+$), we can reach an exhaustion of space. The solution is to keep only the active ones, i.e. the ones showed up (on the edges of implication graph) in the current decision level.
Fig. 3 The breath-taking jump
The following is a copy of original copyright notice of slides where the images here were taken.
Copyright notice: some material (text, figures) displayed in these slides is courtesy of M. Benerecetti, A. Cimatti, P. Pandya, M. Pistore, M. Roveri, and S.Tonetta, who detain its copyright. Some exampes displayed in these slides are taken from [Clarke, Grunberg & Peled, “Model Checking”, MIT Press], and their copyright is detained by the authors. All the other material is copyrighted by Roberto Sebastiani. Every commercial use of this material is strictly forbidden by the copyright laws without the authorization of the authors. No copy of these slides can be displayed in public without containing this copyright notice.
See appendix for credits.
Chronological backtracking is an improvement for the DPLL algorithm backtracking. It can provide multiple jumps back to the assignment tree, while DPLL when there is a conflict, it simply flips the last assigned literal (thus one step).
There are two types of assignment, one is binary decision, the other is unit propagation, which is implied by the decisions. So when we reach a conflict, we jump back to the binary decision point, omitting all the implied assignment caused by that decision.
Assignments are stored in a stack with tags: unit, open, closed. They respectively mean unit-propagation, first try (chances are still there, thus open), second try (no more chances on this literal). When a conflict is met, we pop the stack till the most recent open assignment and toggle it into closed, and continues the search.
The background is a CNF SAT problem. The presented is part of its assignment tree. Red literals are already assigned. We make a binary decision (true) on $A_1$, leading the clauses $c_7$, $c_8$ be satisfied.
Fig. 1
As a consequence, $A_2, A_3, A_4, A_5, A_6$ are unit-propagated in order. But then $c_6$ would be false, reaching a conflict. Hence due to chronological backtracking idea, we remove all these new assignments since $A_1$, and push $\neg A_1$ to the stack.
Fig. 2
The following is a copy of original copyright notice of slides where the images here were taken.
Copyright notice: some material (text, figures) displayed in these slides is courtesy of M. Benerecetti, A. Cimatti, P. Pandya, M. Pistore, M. Roveri, and S.Tonetta, who detain its copyright. Some exampes displayed in these slides are taken from [Clarke, Grunberg & Peled, “Model Checking”, MIT Press], and their copyright is detained by the authors. All the other material is copyrighted by Roberto Sebastiani. Every commercial use of this material is strictly forbidden by the copyright laws without the authorization of the authors. No copy of these slides can be displayed in public without containing this copyright notice.
A single color is the simplest choice, but choosing a color is not simple. Pure white background or black might be mediocre. It can't be too bright, because it is subsidiary as the name indicates.
If we go to ubuntu.com, press ctrl+shift+I (Chrome), navigate to body tag, here it might be
background: #fff url("/sites/ubuntu/latest/u/img/patterns/body_bg.jpg");
If you examine clearly (tilt your screen), body_bg.jpg is not a pure white image, otherwise it would be here. Yep, it is a seamless background image with patterns on it.
credit: ubuntu.com
Under Ubuntu, one may turn to GIMP for such mission (link). An excerpt is to use Filters > Map > Make Seamless, you can test it under Filters > Map > Tile in a bigger canvas (e.g., double-sized). Remind that the seamless background images come in squares so that they can be easily tiled.
credit: ibelieveinadv.com
A 1px stripe is not alluring, but the arrangement of many of them might. See this website for instance (link), it uses
background: #2f2f2f url("http://www.ibelieveinadv.com/commons/stripes.gif");
By default, a background-image is repeated (tiled) both vertically and horizontally.
Indeed, the role of images of large resolution seems blurred, but the effect won't. See worldwildlife.org (link), but the technologies behind should be applied too (Large Images in Rails). A full-size illustration may make your site cuter (link).
The program body is here,
First to mention that a periodic program is that it is activated periodically, i.e. the program wakes up periodically (it is ready for execution). Under Linux kernel, you could trace such wake up events (sched_wake_up) through ftrace. The sample program uses a real-time timer ITIMER_REAL to create periodic interrupts. The timer is set initially 2000000 us (=2s) and thence 5000us (5ms).
start_periodic_timer(2000000, 5000);
In further detail, that is
signal(SIGALRM, sighand);
Notice that sighand is the name of the call-back function. Whenever there a SIGALRM fires within the program, the function sighand is called. Though in the example it is a do-nothing function. The signal function registers sighand as the call-back, but it doesn't execute it.
The following does the job to set periods and the first round offset (this is to ensure the periodicity since we are still initializing the timer before the real periodic part comes). The timer ITIMER_REAL fires the signal SIGALRM when the timer count decreases to zero (expires), as a consequence, signal goes executed.
setitimer(ITIMER_REAL, &t, NULL);
So there are periodic interrupts on which a futile function is run (whence the program wakes up). The following infinite loop does sleeping till the signal is fired (pause()), then an in-genuine job_body() is under way. The job body function is "controlled" within 5ms such that all interrupt signals are captured on-time.
while(1) {
wait_next_activation();
job_body();
}
An implementation of periodic programs follows this pattern,
void *PeriodicTask(void *arg)
{
<initialization>;
<start periodic timer, period = T>;
while (cond) {
<read sensors>;
<update outputs>;
<update state variables>;
<wait next activation>;
}
}
As a sequel of a previous article on timed automaton (link), here we introduce its computational models.
Why region automata? Timed automata have infinite state space (time be divided into infinite pieces), region automata give a finite partition of timed automata such that the computation becomes possible.
Intuition A region is a set of equivalent states. The partition divides the state space into different equivalent classes (regions).
Temporal constraint given by this grammar $\phi := x > c | x < c | x = c | \phi \wedge \phi$, $c$ must be an integer constant (to ensure non-zenoness)
Equivalent class The set of states which satisfies the same set of temporal constraints.
Region equivalence states are equivalent due to being in the same region, they are either within the integer grid, on the $x=c$ or $y=c$ axes, or above/below the diagonal of the integer grid. (see Figure 1.)
Fig 1. Regions as equivalent classes
Remind that largest constant relevant $c$ is actually the ceiling of $x_i$, i.e. $c = \lceil x_i \rceil$. Figure 2 is an example of partitions (regions) of the state space of a timed automaton. Not only are those shadowed areas regions, but also segments of lines (they usually are a result of clock resetting).
Fig 2. Regions on a 2-clock timed automaton
A further example Figure 3 shows the region representation of a simple timed automaton. Location $F$ is shadowed since it may loop forever, a bad design (livelock).
Fig 3. Timed automaton represented in regions
Time-abstract bisimulation If $w \simeq v$, $w,v \in l$, 1) after action $a$, $w'$ is in the region of location $l'$, so is $v'$; 2) $\forall d \exists d' . w+d \simeq v+d'$. They are respectively the transition on action and the transition on delay.
Region equivalence relation is a time-abstract bisimulation ($\simeq$).
Region reset The clock for all equivalent states is reset, hence the operation projects the whole region onto the clock axis (i.e. a line of shadow).
Why zone automata? Regions are still too many, we can force them collapse into unions of regions, where the unions are convex, i.e. no angles are larger than 180 degrees.
Zone Zones are so-called symbolic state (conjunction of regions). Formally, $Z = (s, \varphi)$, that is to start from a location (state) $s$ in a timed automaton, we make a conjunction of regions specified by temporal constraint $\varphi$.
Zone automaton A transition system for zones. Formally, $Z = (Q, Q^0, \Sigma, R)$, set of zones, initial zone, set of transition labels, transition relation.
Symbolic transition It may involve operations such as intersection (conjuncts), delay (stretches diagonally as x,y propagate in time simultaneously), reset (projects a shadow on the time axis). For a zone $Z = (s, \varphi)$, the transition is denoted as $\mathsf{succ}(\varphi, e)$, where $e$ is the label of switch. When $e$ is executed, $Z$ propagates by time till the time constraint $\varphi$ is met. The action is thus invoked. Proceed with a reset if it is needed.
Fig 4. Transitions on Zone Automaton
Figure 4 showed a symbolic transition from location n to m, i.e. $(n, 1 \leqslant x \leqslant 4, 1 \leqslant y \leqslant 3) \rightarrow (m, x>3,y=0)$
The most of this post is heavily extracted from the RS's teaching slides, hence I don't claim the copyright. The character of this post is intended to be a note, with marginal and personal remarks. For those who need to respect the source, please refer the link in the references.
Timed Automaton Intuitively, an automaton with clocks, the transitions from state to state are constrained by time. Formally, $A = (L, L^0, \Sigma, X, I, E)$, respectively the set of locations (states), the set of initial locations, labels, clocks, invariants, the set of edges (transitions) $$E = \{ (s, a, \varphi, \lambda, s') | s,s' \in L, a \in \Sigma, \varphi \text{:clock constraints}, \lambda \subseteq X \}$$
Clock a stopwatch in this context, i.e. clocks are to measure the elapsed time, it can be reset.
Guard Boolean comparison between the clock and some integer value, serves as a constraint for the switch from one location to another
Action the label of transition, used to synchronize actions among several timed automata
Reset set the clock to time 0 and meanwhile the clock starts ticking again
Invariant a time constraint residing inside the state which must be respected when staying within such state, otherwise, it must move out.
Deadlock cases are, there are no more allowed moves (due to bad design of automata).
We quote an automaton from this slide [1],
Figure 1. An Example Timed Automaton
So it comes to this moment that I shall write what a true blogger practices. Not those lifeless pieces of knowledge, not wild copies of diffused computer techniques, or minute excerpts or backup discoveries. After all, after hunting after the ocean of webpages to obtain a very portion of nutrition, one wonders about the behind scenes and how the world bloggers think. Simply, a real person to talk with, on the somewhat crossed paths, or even colleagues of the same kind. You know, the laws of attraction.
The prime purpose of this blog was nothing but put aside some tricks that I came across so that later on I can easily find them. So why this turn? Why didn't I write these lines from the very beginning?
Well, I tried, in my second mother tongue. I was a pride self-assumed writer. I have jotted down many of my own guts, most of them obscure and in an archaic style so that no one except those who know me well could bother reading. My journalist-to-be brother definitely attempted to seek a way to understand me, being elder made him fraternal and faster-matured. We had a geographic segregation since every of us had departed to different universities, his in northwest and mine northeast. The span was the width of China. My mother tongue is a Long dialect. And I quickly mastered Mandarin with the spicy of northeastern accent while I stayed four years in the college. I admit that I have quite a talent of mimicking sounds, but not so much on memory. I was terrified to force myself to remember at grade two. We were asked to recite a short paragraph, only three lines. I had fought so hard but I could not manage. Nonetheless, I grew up, with a rather noteworthy fame at the place. During my university period, I observed and struggled, sought and sighed, alone. We met a few times, each time ended up arguing until both were tired. There was a lack of perception. We are seemingly divided by fate. It lasted until today and I have moved to Europe while he becomes a real news reporter. We haven't talked in depth, only some family greetings. There have not been acknowledgeable comments of my writings. My perplexed groaning was like a grain dropped into a pond. Until one day I was provoked to take off everything from my first blog. The blog host set one post as hidden. I thus wrote a python snippet to scrape out my fruits. My major is Informatics, not to brag. To write a piece of running code you need aches as the same when I construe the very picture in my head and put them into readable words. They do take time more than you could plan. I am still on this steep rising learning curve. I had a plea to terminate the amateur author life. Being in a prestigious European university and studying science you could just accord that writing is too much a luxurious leisure. The reality smashed in my face saying nothing is necessary but survival. Music is just in the background to sooth you in hardship. Parties belong to the drinking dudes. News is all of a manipulation of public thought. Religion, a salvation when you have lost your secular hope and become desperate. Talent for languages in such a multilingual context, a not-so-relevant skill to have for decoding the mystery of mathematics, to mention, Computability and Computational Complexity etc. To speak of truth, right now I am into this far-reaching nearby leisure again. Then why?
To solve this, I need to tell more of my latest deviation from the thesis work. I have taken my liberty to taste the whole of Yann's Life of Pi, so the Ang Lee's film. Shall we put this page down at our feet, and scream we are back?! We will see. I had meant to write a comment of Pi, but what do you see?
Finite Transition System $M = (S, I, R, L)$, respectively the set of states, the set of initial states, the set of transition relations, labels. Simply put, a computational model, similar to Finite State Machine.
Which Computation? Well, model checking. $M \models \varphi$
Why abstraction? Too many states to compute and the abstraction reduces the number of states.
Why abstraction works? The existential-quantified properties (ECTL) are preserved after the abstraction ($M$ simulates $M'$, i.e., $M$ has whatever $M'$ has), that is, $M' \models \varphi \rightarrow M \models \varphi$. (But not vice versa!)
Now let's go to terms.Abstraction function $h: S \rightarrow S'$
Simulation $M$ simulates $M'$ when each transition of $M'$ has a corresponding one in $M$. The simulation is the set of pairs of states $p \subseteq \{ (s,s') | s \in S, s' \in S' \}$ that records such behavior. It is the set denotation of the abstract function $h$.
Bisimulation The simulation applies on both sides. According to property preservation, $M \models \varphi \rightarrow M' \models \varphi$. As a consequence, $M \not \models \varphi \rightarrow M' \not \models \varphi$, otherwise we reach a contradiction.
$M$ simulates $M'$, plainly put, $M$ is an abstraction (simulation) from $M'$.
What about universal-quantified properties? (in LTL or ACTL) They are preserved when $M'$ simulates $M$. That is, $$M' \models \varphi \rightarrow M \models \varphi$$ Yes, same conclusion but different condition. Still, the reverse doesn't hold.
Credit: ~rseba, disi.unitn.it
If we draw a relation $p = \{(S_{ij}, T_i) | \text{for all possible } i,j \}$, we see (with effort) that $p$ is a simulation from $M$ to $M'$ (i.e. $M'$ simulates $M$). Verify it by the rigorous definition, if $(S_{11}, T_1) \in p$, $(S_{11}, S_{12}) \in R_M$, $\exists (T_1, T_1) \in R_{M'}$ s.t. $(S_{12}, T_1) \in p$. So are the rest transition relations of $M$. Hence, the universal-quantified property preservation applies. e.g. if $\varphi$ is pure boolean, $$M' \models \mathbf{AG} \varphi \rightarrow M \models \mathbf{AG} \varphi$$
To note that the reverse doesn't hold. For instance, $(S_{13}, T_1) \in p$, $(T_1, T_1) \in R_{M'}$, $\forall j. \nexists (S_{13},S_{1j}) \in R_{M}$ s.t. $(S_{1j},T_1) \in p$.
With the help of xclip, one can copy the whole text file to the system clipboard
$ sudo apt-get install xclip
The following copys the content of foo file to clipboard (X selection)
$ cat foo | xclip -selection c
xclip -o > foo
This article explains how to compile a sample Linux character device driver and how to read and write from the device.
The sample code is a copy of ldd3's example code sleepy.
/*
* sleepy.c -- the writers awake the readers
*
* Copyright (C) 2001 Alessandro Rubini and Jonathan Corbet
* Copyright (C) 2001 O'Reilly & Associates
*
* The source code in this file can be freely used, adapted,
* and redistributed in source or binary form, so long as an
* acknowledgment appears in derived source files. The citation
* should list that the code comes from the book "Linux Device
* Drivers" by Alessandro Rubini and Jonathan Corbet, published
* by O'Reilly & Associates. No warranty is attached;
* we cannot take responsibility for errors or fitness for use.
*
* $Id: sleepy.c,v 1.7 2004/09/26 07:02:43 gregkh Exp $
*/
#include <linux/module.h>
#include <linux/init.h>
#include <linux/sched.h> /* current and everything */
#include <linux/kernel.h> /* printk() */
#include <linux/fs.h> /* everything... */
#include <linux/types.h> /* size_t */
#include <linux/wait.h>
MODULE_LICENSE("Dual BSD/GPL");
static int sleepy_major = 0;
static DECLARE_WAIT_QUEUE_HEAD(wq);
static int flag = 0;
ssize_t sleepy_read (struct file *filp, char __user *buf, size_t count, loff_t *pos)
{
printk(KERN_DEBUG "process %i (%s) going to sleep\n",
current->pid, current->comm);
wait_event_interruptible(wq, flag != 0);
flag = 0;
printk(KERN_DEBUG "awoken %i (%s)\n", current->pid, current->comm);
return 0; /* EOF */
}
ssize_t sleepy_write (struct file *filp, const char __user *buf, size_t count,
loff_t *pos)
{
printk(KERN_DEBUG "process %i (%s) awakening the readers...\n",
current->pid, current->comm);
flag = 1;
wake_up_interruptible(&wq);
return count; /* succeed, to avoid retrial */
}
struct file_operations sleepy_fops = {
.owner = THIS_MODULE,
.read = sleepy_read,
.write = sleepy_write,
};
int sleepy_init(void)
{
int result;
/*
* Register your major, and accept a dynamic number
*/
result = register_chrdev(sleepy_major, "sleepy", &sleepy_fops);
if (result < 0)
return result;
if (sleepy_major == 0)
sleepy_major = result; /* dynamic */
return 0;
}
void sleepy_cleanup(void)
{
unregister_chrdev(sleepy_major, "sleepy");
}
module_init(sleepy_init);
module_exit(sleepy_cleanup);
obj-m = sleepy.o KVERSION = $(shell uname -r) PWD = $(shell pwd) all: make -C /lib/modules/$(KVERSION)/build M=$(PWD) modules clean: make -C /lib/modules/$(KVERSION)/build M=$(PWD) clean
The ultimate way is to compile it along with a built kernel tree. However, for the time being, installing Linux kernel headers would suffice. It should already be installed by default.
sudo apt-get install linux-headers-$(uname -r)
If installed, type
make
You will see some new files are generated, including sleepy.ko, to load this module
sudo insmod sleepy.ko
To unload,
sudo rmmod sleepy
The sleepy is created with a dynamic major, we need to create a device file for it. First get the major number,
$ cat /proc/devices | grep sleepy 250 sleepy
Then create a node under /dev, c is to create a character file, 0 is its minor number.
sudo mknod /dev/sleepy c 250 0
Now we can read and write the device using C library function read, write, or from shell
echo "sleep" > /dev/sleepy cat /dev/sleepy
Though what sleepy does is that it makes the reader process fall asleep while the writer process wakes all readers up.
#include <fcntl.h>
#include <unistd.h>
int fd;
char buffer[32];
fd = open("/dev/sleepy", O_RDONLY);
read(fd,buffer,10);
language support, click Install/Remove Lanugages button, and select Tibetan from the list, then Apply Changes.
Notebook: Dell INSPIRON 1564. There was no such problem in Ubuntu 11.04. Don't upgrade to 12.10, you will encounter ugly interface problem (see here).
Noticed from here: askubuntu, a method was proposed, which was to modify a line in /etc/default/grub into
GRUB_CMDLINE_LINUX_DEFAULT="quiet splash acpi_backlight=vendor acpi_osi=Linux"And then update and reboot
sudo update-grub sudo reboot
Although I tried the same, I don't confirm this will definitely work. My experience is, if you tap slowly one at a time until it changes the brightness and show the notification, then proceed, it will be okay. If you are stuck in such freezing state, any keyboard combo can't save you out.
That is what I wanted to do. Ubuntu didn't save (or the video driver) the last-time configuration of brightness. (link)
The solution, I too confirm, is to add a local script to be executed on reboot. Here is the excerpt.
sudo vi /etc/rc.local
Add the following due to your folders under /sys/class/backlight (you might need play around with it)
echo 0 > /sys/class/backlight/acpi_video0/brightness exit 0
My machine uses a default video driver (non-proprietary) and the video card ATI RV710.
grep "foo\|bar" grep -E "foo|bar" egrep "foo|bar" grep -e foo -e bar
grep foo | grep bar
grep -v foo
This app is basically a link to a website.
Create manifest.json with the following content
{
"name": "BBC News",
"description": "BBC World News",
"version": "1",
"manifest_version": 2,
"icons": { "128": "bbc-icon-128.png" },
"app": {
"urls":[
"http://www.bbc.com/news"
],
"launch": {
"web_url": "http://www.bbc.com/news"
}
}
}
I got this icon,
At chrome://extensions/, turn on Developer Mode, and click Load unpacked extension, locate the folder, that's it!