Ranking Functions for Vector Addition Systems

Vector addition systems are an important model in theoretical computer science and have been used for the analysis of systems in a variety of areas. Termination is a crucial property of vector addition systems and has received considerable interest in the literature. In this paper we give a complete method for the construction of ranking functions for vector addition systems with states. The interest in ranking functions is motivated by the fact that ranking functions provide valuable additional information in case of termination: They provide an explanation for the progress of the vector addition system, which can be reported to the user of a verification tool, and can be used as certificates for termination. Moreover, we show how ranking functions can be used for the computational complexity analysis of vector addition systems (here complexity refers to the number of steps the vector addition system under analysis can take in terms of the given initial vector)

Decidable Models of Recursive Asynchronous Concurrency

Asynchronously communicating pushdown systems (ACPS) that satisfy the empty-stack constraint (a pushdown process may receive only when its stack is empty) are a popular decidable model for recursive programs with asynchronous atomic procedure calls. We study a relaxation of the empty-stack constraint for ACPS that permits concurrency and communication actions at any stack height, called the shaped stack constraint, thus enabling a larger class of concurrent programs to be modelled. We establish a close connection between ACPS with shaped stacks and a novel extension of Petri nets: Nets with Nested Coloured Tokens (NNCTs). Tokens in NNCTs are of two types: simple and complex. Complex tokens carry an arbitrary number of coloured tokens. The rules of NNCT can synchronise complex and simple tokens, inject coloured tokens into a complex token, and eject all tokens of a specified set of colours to predefined places. We show that the coverability problem for NNCTs is Tower-complete. To our knowledge, NNCT is the first extension of Petri nets, in the class of nets with an infinite set of token types, that has primitive recursive coverability. This result implies Tower-completeness of coverability for ACPS with shaped stacks

The Well Structured Problem for Presburger Counter Machines

International audienceWe introduce the well structured problem as the question of whether a model (here a counter machine) is well structured (here for the usual ordering on integers). We show that it is undecidable for most of the (Presburger-defined) counter machines except for Affine VASS of dimension one. However, the strong well structured problem is decidable for all Presburger counter machines. While Affine VASS of dimension one are not, in general, well structured, we give an algorithm that computes the set of predecessors of a configuration; as a consequence this allows to decide the well structured problem for 1-Affine VASS

An algebraic approach to energy problems II - the algebra of energy functions

Energy and resource management problems are important in areas such as embedded systems or autonomous systems. They are concerned with the question whether a given system admits infinite schedules during which certain tasks can be repeatedly accomplished and the system never runs out of energy (or other resources). In order to develop a general theory of energy problems, we introduce energy automata: finite automata whose transitions are labeled with energy functions which specify how energy values change from one system state to another. We show that energy functions form a *-continuous Kleene ω-algebra, as an application of a general result that finitely additive, locally *-closed and T-continuous functions on complete lattices form *-continuous Kleene ω-algebras. This permits to solve energy problems in energy automata in a generic, algebraic way. In order to put our work in context, we also review extensions of energy problems to higher dimensions and to games

Vérification efficace de systèmes à compteurs à l'aide de relaxations

Abstract : Counter systems are popular models used to reason about systems in various fields such as the analysis of concurrent or distributed programs and the discovery and verification of business processes. We study well-established problems on various classes of counter systems. This thesis focusses on three particular systems, namely Petri nets, which are a type of model for discrete systems with concurrent and sequential events, workflow nets, which form a subclass of Petri nets that is suited for modelling and reasoning about business processes, and continuous one-counter automata, a novel model that combines continuous semantics with one-counter automata. For Petri nets, we focus on reachability and coverability properties. We utilize directed search algorithms, using relaxations of Petri nets as heuristics, to obtain novel semi-decision algorithms for reachability and coverability, and positively evaluate a prototype implementation. For workflow nets, we focus on the problem of soundness, a well-established correctness notion for such nets. We precisely characterize the previously widely-open complexity of three variants of soundness. Based on our insights, we develop techniques to verify soundness in practice, based on reachability relaxation of Petri nets. Lastly, we introduce the novel model of continuous one-counter automata. This model is a natural variant of one-counter automata, which allows reasoning in a hybrid manner combining continuous and discrete elements. We characterize the exact complexity of the reachability problem in several variants of the model.Les systèmes à compteurs sont des modèles utilisés afin de raisonner sur les systèmes de divers domaines tels l’analyse de programmes concurrents ou distribués, et la découverte et la vérification de systèmes d’affaires. Nous étudions des problèmes bien établis de différentes classes de systèmes à compteurs. Cette thèse se penche sur trois systèmes particuliers : les réseaux de Petri, qui sont un type de modèle pour les systèmes discrets à événements concurrents et séquentiels ; les « réseaux de processus », qui forment une sous-classe des réseaux de Petri adaptée à la modélisation et au raisonnement des processus d’affaires ; les automates continus à un compteur, un nouveau modèle qui combine une sémantique continue à celles des automates à un compteur. Pour les réseaux de Petri, nous nous concentrons sur les propriétés d’accessibilité et de couverture. Nous utilisons des algorithmes de parcours de graphes, avec des relaxations de réseaux de Petri comme heuristiques, afin d’obtenir de nouveaux algorithmes de semi-décision pour l’accessibilité et la couverture, et nous évaluons positivement un prototype. Pour les «réseaux de processus», nous nous concentrons sur le problème de validité, une notion de correction bien établie pour ces réseaux. Nous caractérisions précisément la complexité calculatoire jusqu’ici largement ouverte de trois variantes du problème de validité. En nous basant sur nos résultats, nous développons des techniques pour vérifier la validité en pratique, à l’aide de relaxations d’accessibilité dans les réseaux de Petri. Enfin, nous introduisons le nouveau modèle d’automates continus à un compteur. Ce modèle est une variante naturelle des automates à un compteur, qui permet de raisonner de manière hybride en combinant des éléments continus et discrets. Nous caractérisons la complexité exacte du problème d’accessibilité dans plusieurs variantes du modèle

Foundations of Software Science and Computation Structures

This open access book constitutes the proceedings of the 23rd International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2020, which took place in Dublin, Ireland, in April 2020, and was held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2020. The 31 regular papers presented in this volume were carefully reviewed and selected from 98 submissions. The papers cover topics such as categorical models and logics; language theory, automata, and games; modal, spatial, and temporal logics; type theory and proof theory; concurrency theory and process calculi; rewriting theory; semantics of programming languages; program analysis, correctness, transformation, and verification; logics of programming; software specification and refinement; models of concurrent, reactive, stochastic, distributed, hybrid, and mobile systems; emerging models of computation; logical aspects of computational complexity; models of software security; and logical foundations of data bases.

Foundations of Software Science and Computation Structures

This open access book constitutes the proceedings of the 23rd International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2020, which took place in Dublin, Ireland, in April 2020, and was held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2020. The 31 regular papers presented in this volume were carefully reviewed and selected from 98 submissions. The papers cover topics such as categorical models and logics; language theory, automata, and games; modal, spatial, and temporal logics; type theory and proof theory; concurrency theory and process calculi; rewriting theory; semantics of programming languages; program analysis, correctness, transformation, and verification; logics of programming; software specification and refinement; models of concurrent, reactive, stochastic, distributed, hybrid, and mobile systems; emerging models of computation; logical aspects of computational complexity; models of software security; and logical foundations of data bases.

Foundations of Software Science and Computation Structures

This open access book constitutes the proceedings of the 22nd International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2019, which took place in Prague, Czech Republic, in April 2019, held as part of the European Joint Conference on Theory and Practice of Software, ETAPS 2019. The 29 papers presented in this volume were carefully reviewed and selected from 85 submissions. They deal with foundational research with a clear significance for software science