Commit 496c449f authored by Alexandre Duret-Lutz's avatar Alexandre Duret-Lutz
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Update the intro of tl.tex, and add a reference to VECOS'11.

* doc/tl/tl.tex, doc/tl/tl.bib: Here.
parent 776564cb
......@@ -77,6 +77,26 @@
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,
author = {Cindy Eisner and Dana Fisman},
title = {A Practical Introduction to {PSL}},
......
......@@ -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
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
$A^\star=\cup_{n\in\N}A^n$ 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
$|\sigma|=n$.
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
subsequence built using letters from $\sigma(i)$ to $\sigma(j)$. If
$\sigma$ is infinite, we denote $\sigma^{i..}$ the suffix of $\sigma$
......@@ -221,23 +217,18 @@ starting at letter $\sigma(i)$.
\section{Usage in Model Checking}
The temporal formul\ae{} described in this document, and used by Spot,
should be interpreted on a behavior (or an execution) of the system to
verify. The idea of model checking is that we want to ensure that a
formula (the property to verify) holds on all possibles behaviors of
the system.
In this document we will describe the syntax of the temporal
formul\ae{} used in Spot, and give their interpretation on an infinite
sequence.
The temporal formul\ae{} described in this document, should be
interpreted on behaviors (or executions, or scenarios) of the system
to verify. In model checking we want to ensure that a formula (the
property to verify) holds on all possibles behaviors of the system.
If we model the system as some sort of giant automaton, where each
state represent a configuration of the system, a behavior of the
system can be represented by an infinite sequence of configurations.
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.
If we model the system as some sort of giant automaton (e.g., a Kripke
structure) where each state represent a configuration of the system, a
behavior of the system can be represented by an infinite sequence of
configurations. Each configuration can be described by an affectation
of some proposition variables that we will call \emph{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
$\AP=\{r,y,g\}$. 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
configurations. In other words: $\sigma\in(\B^\AP)^\omega$.
When a formula $\varphi$ holds on an \emph{infinite} sequence $\sigma$, we
will write $\sigma \vDash \varphi$ (read as $\sigma$ is a model of
$\varphi$).
When a formula $\varphi$ holds on an \emph{infinite} sequence
$\sigma$, we write $\sigma \vDash \varphi$ (read as $\sigma$ is a
model of $\varphi$).
When a formula $\varphi$ holds on an \emph{finite} sequence $\sigma$, we
will write $\sigma \VDash \varphi$.
When a formula $\varphi$ holds on an \emph{finite} sequence $\sigma$,
we write $\sigma \VDash \varphi$.
\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 $\M$
operators using the following two rewritings:
\begin{align*}
f \W g&\equiv g \R (g \OR f)\\
f \M g&\equiv g \U (g \AND f)
\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}
......
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