Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2207.07479

Zone-based verification of timed automata: extrapolations, simulations and what next?

Patricia Bouyer·Paul Gastin·Frédéric Herbreteau·Ocan Sankur·B. Srivathsan
View original source ↗Read source document ↗Export metadata ↓

Abstract

Timed automata have been introduced by Rajeev Alur and David Dill in the early 90's. In the last decades, timed automata have become the de facto model for the verification of real-time systems. Algorithms for timed automata are based on the traversal of their state-space using zones as a symbolic representation. Since the state-space is infinite, termination relies on finite abstractions that yield a finite representation of the reachable states. The first solution to get finite abstractions was based on extrapolations of zones, and has been implemented in the industry-strength tool Uppaal. A different approach based on simulations between zones has emerged in the last ten years, and has been implemented in the fully open source tool TChecker. The simulation-based approach has led to new efficient algorithms for reachability and liveness in timed automata, and has also been extended to richer models like weighted timed automata, and timed automata with diagonal constraints and updates. In this article, we survey the extrapolation and simulation techniques, and discuss some open challenges for the future.

Explore related subjects

cs.LO

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Patricia Bouyer, Paul Gastin, Frédéric Herbreteau, Ocan Sankur, B. Srivathsan. 2022-07-15. Zone-based verification of timed automata: extrapolations, simulations and what next?. https://arxiv.org/abs/2207.07479

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Arithmetics within the Linear Time Hierarchy

We identify fragments of the arithmetic $S_1$ that enjoy nice closure properties and have exact characterization of their definable multifunctions. To do this, in the language of $S_1$, $L_1$, starting from the formula classes, $Σ^{\mathsf b}_{i}$, which ignore sharply bounded quantifiers when determining quantifier alternations, we define new syntactic classes by counting bounded existential sharply bounded universal quantifiers blocks. Using these, we define arithmetics: $\breve{S}^{i}_{1}$, $TLS^i_1$ and $TSC^i_1$. $\breve{S}^{i}_{1}$ consists of open axioms for the language symbols and length induction for one of our new classes, $SIUT_{i,1}^{\{p(|id|)\}}$. $TLS^i_1$ and $TSC^i_1$ are defined using axioms related to dependent choice sequences for formulas from two other classes within $Σ^{\mathsf b}_{i}$. We prove for $i \geq 1$ that $$TLS^i_1 \subseteq TSC^i_1 \subseteq \breve{S}^{i}_{1} \preceq_{\forall B(SITT_{i+1}^{\{p(|id|)\}})} TLS^{i+1}_1$$ and that the $SITT_{i}^{\{p(|id|)\}}$-definable in $TLS^i_1$ (resp. $SITT_{i}^{\{2^{p(||id||)}\}}$-definable in $TSC^i_1$) multifunctions are $L_1$-$FLOGSPACE^{SIT_{i,1}}[wit]$ (resp. $L_1$-$FSC^{SIT_{i,1}}[wit]$). These multifunction classes are respectively the logspace or $SC$ (poly-time, polylog-space) computable multifunctions whose output is bound by a term in $L_1$ and that have access to a witness oracle for another restriction on the $Σ^{\mathsf b}_{i}$ formulas, $SIT_{i,1}$. For the $i=1$ cases, this simplifies respectively to the functions in logspace and $SC$, Steve's Class, poly-time, polylog-space. We prove independence results related to the Matiyasevich Robinson Davis Putnam Theorem (MRDP) and to whether our theories prove simultaneous nondeterministic polynomial time, sublinear space is equal to co-nondeterministic polynomial time, sublinear space.

cs.LO↗
arXiv2026

TREBL -- A Relative Complete Temporal Event-B Logic. Part I: Theory

The verification of liveness conditions is an important aspect of state-based rigorous methods. This article addresses the extension of the logic of Event-B to a powerful logic, in which properties of traces of an Event-B machine can be expressed. However, all formulae of this logic are still interpreted over states of an Event-B machine rather than traces. The logic exploits that for an Event-B machine $M$ a state $S$ determines all traces of $M$ starting in $S$. We identify a fragment called TREBL of this logic, in which all liveness conditions of interest can be expressed, and define a set of sound derivation rules for the fragment. We further show relative completeness of these derivation rules in the sense that for every valid entailment of a formula $φ$ one can find a derivation, provided the machine $M$ is sufficiently refined. The decisive property is that certain variant terms must be definable in the refined machine. We show that such refinements always exist. Throughout the article several examples from the field of security are used to illustrate the theory.

cs.LO↗
arXiv2026

Scenes: A Meta-Logical Algebra for Mutable State

Modelling of mutable state spaces and precisely describing how variables are manipulated in a program is a fundamental problem in compositional verification. Though we can make use of the embedded abstract syntax of a program for such analysis, this runs contrary to the shallow-embedding approach, and hampers efficient proof automation. On the other hand, lenses and prisms provide an elegant algebraic foundation for modelling state, which provide sufficient structure to provide meta-logical program analysis, but without requiring a deep embedding. Nevertheless lenses, as complex algebraic objects, cannot easily be combined, complemented, or collected in sets. In this paper we contribute an accompanying algebraic structure called the scene, which allows us to characterise the set of variables, or coordinates, in a state space. Scenes intuitively correspond to sets of lenses, but like lenses they are purely semantic algebraic objects. We demonstrate that scenes provide us with sufficient structure to characterise the lens-based meta-logical properties, like independence and equivalence. Moreover, we introduce the notion of a scene space, analogous to a vector space, which allows us to recover a set-like algebraic structure. Finally, we show how scenes allow us to characterise the free and bound variables of expressions and programs, without any need for syntax, and demonstrate their use for reasoning about programs by deriving reasoning principles for the parallel composition operator.

cs.LO↗