A basic tool for the modeling of Marked-Controlled Reconfigurable Petri Nets

In previous studies, we have introduced marked-controlled net rewriting systems and a subclass of these called marked-controlled reconfigurable Petri nets. In a marked-controlled net rewriting system, a system configuration is described as a Petri net, and a change in configuration is described as a graph rewriting rule. A marked-controlled reconfigurable Petri net is a marked-controlled net rewriting system where a change in configuration amounts to a modification in the flow relations of the places in the domain of the involved rule in accordance with this rule, independently of the context in which this rewriting applies. In both models, the enabling of a rule not only depends on the net topology, but also depends on the net marking according to control places. Even though the expressiveness of Petri nets and marked-controlled reconfigurable Petri nets is the same, with marked-controlled reconfigurable Petri nets, we can easily and directly model concurrent and distributed systems that change their structure dynamically. In this article, we present MCReNet, a tool for the modeling and verification of marked-controlled reconfigurable Petri nets

About Decisiveness of Dynamic Probabilistic Models

Decisiveness of infinite Markov chains with respect to some (finite or infinite) target set of states is a key property that allows to compute the reachability probability of this set up to an arbitrary precision. Most of the existing works assume constant weights for defining the probability of a transition in the considered models. However numerous probabilistic modelings require the (dynamic) weight to also depend on the current state. So we introduce a dynamic probabilistic version of counter machine (pCM). After establishing that decisiveness is undecidable for pCMs even with constant weights, we study the decidability of decisiveness for subclasses of pCM. We show that, without restrictions on dynamic weights, decisiveness is undecidable with a single state and single counter pCM. On the contrary with polynomial weights, decisiveness becomes decidable for single counter pCMs under mild conditions. Then we show that decisiveness of probabilistic Petri nets (pPNs) with polynomial weights is undecidable even when the target set is upward-closed unlike the case of constant weights. Finally we prove that the standard subclass of pPNs with a regular language is decisive with respect to a finite set whatever the kind of weights

Forward Analysis for WSTS, Part III: Karp-Miller Trees

This paper is a sequel of "Forward Analysis for WSTS, Part I: Completions" [STACS 2009, LZI Intl. Proc. in Informatics 3, 433-444] and "Forward Analysis for WSTS, Part II: Complete WSTS" [Logical Methods in Computer Science 8(3), 2012]. In these two papers, we provided a framework to conduct forward reachability analyses of WSTS, using finite representations of downward-closed sets. We further develop this framework to obtain a generic Karp-Miller algorithm for the new class of very-WSTS. This allows us to show that coverability sets of very-WSTS can be computed as their finite ideal decompositions. Under natural effectiveness assumptions, we also show that LTL model checking for very-WSTS is decidable. The termination of our procedure rests on a new notion of acceleration levels, which we study. We characterize those domains that allow for only finitely many accelerations, based on ordinal ranks

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

The Complexity of Reachability in Affine Vector Addition Systems with States

Vector addition systems with states (VASS) are widely used for the formal verification of concurrent systems. Given their tremendous computational complexity, practical approaches have relied on techniques such as reachability relaxations, e.g., allowing for negative intermediate counter values. It is natural to question their feasibility for VASS enriched with primitives that typically translate into undecidability. Spurred by this concern, we pinpoint the complexity of integer relaxations with respect to arbitrary classes of affine operations. More specifically, we provide a trichotomy on the complexity of integer reachability in VASS extended with affine operations (affine VASS). Namely, we show that it is NP-complete for VASS with resets, PSPACE-complete for VASS with (pseudo-)transfers and VASS with (pseudo-)copies, and undecidable for any other class. We further present a dichotomy for standard reachability in affine VASS: it is decidable for VASS with permutations, and undecidable for any other class. This yields a complete and unified complexity landscape of reachability in affine VASS. We also consider the reachability problem parameterized by a fixed affine VASS, rather than a class, and we show that the complexity landscape is arbitrary in this setting

Modélisation et simulation de processus de biologie moléculaire basée sur les réseaux de Pétri : une revue de littérature

Les réseaux de Pétri sont une technique de simulation à événements discrets développée pour la représentation de systèmes et plus particulièrement de leurs propriétés de concurrence et de synchronisation. Différentes extensions à la théorie initiale de cette méthode ont été utilisées pour la modélisation de processus de biologie moléculaire et de réseaux métaboliques. Il s’agit des extensions stochastiques, colorées, hybrides et fonctionnelles. Ce document fait une première revue des différentes approches qui ont été employées et des systèmes biologiques qui ont été modélisés grâce à celles-ci. De plus, le contexte d’application et les objectif s de modélisation de chacune sont discutés

Acyclic Petri and workflow nets with resets

In this paper we propose two new subclasses of Petri nets with resets, for which the reachability and coverability problems become tractable. Namely, we add an acyclicity condition that only applies to the consumptions and productions, not the resets. The first class is acyclic Petri nets with resets, and we show that coverability is PSPACE-complete for them. This contrasts the known Ackermann-hardness for coverability in (not necessarily acyclic) Petri nets with resets. We prove that the reachability problem remains undecidable for acyclic Petri nets with resets. The second class concerns workflow nets, a practically motivated and natural subclass of Petri nets. Here, we show that both coverability and reachability in acyclic workflow nets with resets are PSPACE-complete. Without the acyclicity condition, reachability and coverability in workflow nets with resets are known to be equally hard as for Petri nets with resets, that being Ackermann-hard and undecidable, respectively

Petri net modelling of a communications protocol

The Petri net is a formal modelling tool applicable to distributed systems and communication protocols. Two methods of analysis are applied to formal models of the "Alternating Bit Protocol". (i) A timed Petri net model is simulated to measure protocol performance. (ii) A modular numeric Petri net model is validated by reachability analysis. The simulation and validation tools are programmed in (i) "C" language and (ii) Prolog. A specification language "Needle" is developed. It describes the model system as a hierarchy of modular state transition networks. The model is searched for all possible event sequences, and the result displayed as a reachability tree. The specification language is capable of describing models which execute backwards in simulation time. The modular numeric Petri net is the basis of a powerful computer architecture, capable of parsing its own specification language to build complex models. Attention is drawn to the similarities between Petri net theory and quantum mechanics