alarsyo/spot
1
0
Fork 0
Code Issues Pull requests Projects Releases Wiki Activity

Update the intro of tl.tex, and add a reference to VECOS'11.

Browse source 
* doc/tl/tl.tex, doc/tl/tl.bib: Here.
This commit is contained in:
Alexandre Duret-Lutz 2012-04-29 23:12:42 +02:00
parent 776564cbf2
commit 496c449fa4
2 changed files with 40 additions and 27 deletions
Download patch file Download diff file Expand all files Collapse all files

20
doc/tl/tl.bib
View file

@ -77,6 +77,26 @@
note = {\url{https://es.fbk.eu/people/tonetta/tests/tcad07/}} note = {\url{https://es.fbk.eu/people/tonetta/tests/tcad07/}}
} }
@InProceedings{ duret.11.vecos,
author = {Alexandre Duret-Lutz},
title = {{LTL} Translation Improvements in {Spot}},
booktitle = {Proceedings of the 5th International Workshop on
Verification and Evaluation of Computer and Communication
Systems (VECoS'11)},
year = {2011},
series = {Electronic Workshops in Computing},
address = {Tunis, Tunisia},
month = sep,
publisher = {British Computer Society},
abstract = {Spot is a library of model-checking algorithms. This paper
focuses on the module translating LTL formul{\ae} into
automata. We discuss improvements that have been
implemented in the last four years, we show how Spot's
translation competes on various benchmarks, and we give
some insight into its implementation.},
url = {http://ewic.bcs.org/category/15853}
}
@Book{ eisner.06.psl, @Book{ eisner.06.psl,
author = {Cindy Eisner and Dana Fisman}, author = {Cindy Eisner and Dana Fisman},
title = {A Practical Introduction to {PSL}}, title = {A Practical Introduction to {PSL}},

47
doc/tl/tl.tex
View file

@ -206,14 +206,10 @@ element $\sigma(i)\in A$. The sequence of length $0$ is a particular
sequence called the \textit{empty word} and denoted $\varepsilon$. We sequence called the \textit{empty word} and denoted $\varepsilon$. We
denote $A^n$ the set of all sequences of length $n$ on $A$ (in denote $A^n$ the set of all sequences of length $n$ on $A$ (in
particular $A^\omega$ is the set of infinite sequences on $A$), and particular $A^\omega$ is the set of infinite sequences on $A$), and
$A^\star=\cup_{n\in\N}A^n$ denotes the set of all finite sequences. $A^\star=\bigcup_{n\in\N}A^n$ denotes the set of all finite sequences.
The length of $n\in\N\cup\{\omega\}$ any sequence $\sigma$ is noted The length of $n\in\N\cup\{\omega\}$ any sequence $\sigma$ is noted
$|\sigma|=n$. $|\sigma|=n$.
For any set $A$, we note $E^\star$ the set of finite sequence
built by concatenating elements of $E$, and $E^\omega$ is set of
infinite sequence over $E$.
For any sequence $\sigma$, we denote $\sigma^{i..j}$ the finite For any sequence $\sigma$, we denote $\sigma^{i..j}$ the finite
subsequence built using letters from $\sigma(i)$ to $\sigma(j)$. If subsequence built using letters from $\sigma(i)$ to $\sigma(j)$. If
$\sigma$ is infinite, we denote $\sigma^{i..}$ the suffix of $\sigma$ $\sigma$ is infinite, we denote $\sigma^{i..}$ the suffix of $\sigma$
@ -221,23 +217,18 @@ starting at letter $\sigma(i)$.
\section{Usage in Model Checking} \section{Usage in Model Checking}
The temporal formul\ae{} described in this document, and used by Spot, The temporal formul\ae{} described in this document, should be
should be interpreted on a behavior (or an execution) of the system to interpreted on behaviors (or executions, or scenarios) of the system
verify. The idea of model checking is that we want to ensure that a to verify. In model checking we want to ensure that a formula (the
formula (the property to verify) holds on all possibles behaviors of property to verify) holds on all possibles behaviors of the system.
the system.
In this document we will describe the syntax of the temporal If we model the system as some sort of giant automaton (e.g., a Kripke
formul\ae{} used in Spot, and give their interpretation on an infinite structure) where each state represent a configuration of the system, a
sequence. behavior of the system can be represented by an infinite sequence of
configurations. Each configuration can be described by an affectation
If we model the system as some sort of giant automaton, where each of some proposition variables that we will call \emph{atomic
state represent a configuration of the system, a behavior of the propositions}. For instance $r=1,y=0,g=0$ describes the
system can be represented by an infinite sequence of configurations. configuration of a traffic light with only the red light turned on.
Each configuration can be described as an affectation of some
proposition variables that we will call atomic propositions. For
instance $r=1,y=0,g=0$ describes the configuration of a traffic light
with only the red light turned on.
Let $\AP$ be a set of atomic propositions, for instance Let $\AP$ be a set of atomic propositions, for instance
$\AP=\{r,y,g\}$. A configuration of the model is a function $\AP=\{r,y,g\}$. A configuration of the model is a function
@ -247,12 +238,12 @@ $\rho:\AP\to\B$ (or $\rho\in\B^\AP$) that associates a truth value
A behavior of the model is an infinite sequence $\sigma$ of such A behavior of the model is an infinite sequence $\sigma$ of such
configurations. In other words: $\sigma\in(\B^\AP)^\omega$. configurations. In other words: $\sigma\in(\B^\AP)^\omega$.
When a formula $\varphi$ holds on an \emph{infinite} sequence $\sigma$, we When a formula $\varphi$ holds on an \emph{infinite} sequence
will write $\sigma \vDash \varphi$ (read as $\sigma$ is a model of $\sigma$, we write $\sigma \vDash \varphi$ (read as $\sigma$ is a
$\varphi$). model of $\varphi$).
When a formula $\varphi$ holds on an \emph{finite} sequence $\sigma$, we When a formula $\varphi$ holds on an \emph{finite} sequence $\sigma$,
will write $\sigma \VDash \varphi$. we write $\sigma \VDash \varphi$.
\chapter{Temporal Syntax} \chapter{Temporal Syntax}
@ -553,11 +544,13 @@ section~\ref{sec:unabbbool} as well as the following two rewritings:
The `\verb=unabbreviate_wm()=` function removes only the $\W$ and $\M$ The `\verb=unabbreviate_wm()=` function removes only the $\W$ and $\M$
operators using the following two rewritings: operators using the following two rewritings:
\begin{align*} \begin{align*}
f \W g&\equiv g \R (g \OR f)\\ f \W g&\equiv g \R (g \OR f)\\
f \M g&\equiv g \U (g \AND f) f \M g&\equiv g \U (g \AND f)
\end{align*} \end{align*}
Among all the possible rewritings (see Appendix~\ref{sec:ltl-equiv})
those two were chosen because they are easier to translate in a
tableau construction~\cite[Fig.~11]{duret.11.vecos}.
\section{SERE Operators} \section{SERE Operators}