A Concurrency-Preserving Translation from Time Petri Nets to Networks of Timed Automata

International audienceSeveral formalisms to model distributed real-time systems coexist in the literature. This naturally induces a need to compare their expressiveness and to translate models from one formalism to another when possible. The first formal comparisons of the expressiveness of these models focused on the preservation of the sequential behavior of the models, using notions like timed language equivalence or timed bisimilarity. They do not consider preservation of concurrency. In this paper we define timed traces as a partial order representation of executions of our models for real-time distributed systems. Timed traces provide an alternative to timed words, and take the distribution of actions into account. We propose a translation between two popular formalisms that describe timed concurrent systems: 1-bounded time Petri nets (TPN) and networks of timed automata (NTA). Our translation preserves the distribution of actions, that is we require that if the TPN represents the product of several components (called processes), then each process should have its counterpart as one timed automaton in the resulting NTA

La concurrence dans les systèmes temps-réel distribués

This thesis is concerned with the modeling and the analysis of distributedreal-time systems. In distributed systems, components evolve partlyindependently: concurrent actions may be performed in any order, withoutinfluencing each other and the state reached after these actions does notdepends on the order of execution. The time constraints in distributed real-timesystems create complex dependencies between the components and the events thatoccur. So far, distributed real-time systems have not been deeply studied, andin particular the distributed aspect of these systems is often left aside. Thisthesis explores distributed real-time systems. Our work on distributed real-timesystems is based on two formalisms: time Petri nets and networks of timedautomata, and is divided into two parts.In the first part, we highlight the differences between centralized anddistributed timed systems. We compare the main formalisms and their extensions,with a novel approach that focuses on the preservation of concurrency. Inparticular, we show how to translate a time Petri net into a network of timedautomata with the same distributed behavior. We then study a concurrency relatedproblem: shared clocks in networks of timed automata can be problematic when oneconsiders the implementation of a model on a multi-core architecture. We showhow to avoid shared clocks while preserving the distributed behavior, when thisis possible.In the second part, we focus on formalizing the dependencies between events inpartial order representations of the executions of Petri nets and time Petrinets. Occurrence nets is one of these partial order representations, and theirstructure directly provides the causality, conflict and concurrency relationsbetween events. However, we show that, even in the untimed case, some logicaldependencies between event occurrences are not directly described by thesestructural relations. After having formalized these logical dependencies, wesolve the following synthesis problem: from a formula that describes a set ofruns, we build an associated occurrence net. Then we study the logicalrelations in a simplified timed setting and show that time creates complexdependencies between event occurrences. These dependencies can be used to definea canonical unfolding, for this particular timed setting.Cette thèse s'intéresse à la modélisation et à l'analyse dessystèmes temps-réel distribués.Un système distribué est constitué de plusieurs composantsqui évoluent de manière partiellement indépendante. Lorsque des actionsexécutables par différentscomposants sont indépendantes, elles sont dites concurrentes.Dans ce cas, elles peuvent être exécutées dans n'importe quel ordre, sanss'influencer, et l'état atteint après ces actions ne dépend pas de leur ordred'exécution.Dans les systèmes temps-réel distribués, les contraintes de temps créent desdépendances complexes entre les composants et les événements qui ont lieu surces composants. Malgré l'omniprésence et l'aspect critique de ces systèmes,beaucoup de leurs propriétés restent encore à étudier.En particulier, la nature distribuée de ces systèmes est souvent laissée de côté.Notre travail s'appuie sur deux formalismesde modélisation: les réseaux de Petri temporels et les réseaux d'automatestemporisés, et est divisé en deux parties.Dans la première partie, nous mettons en évidence les différences entre lessystèmes temporisés centralisés et les systèmes temporisés distribués. Nouscomparons les formalismes principaux et leurs extensions, avec une approcheoriginale qui considère la concurrence.En particulier, nous montrons comment transformer un réseau de Petri temporelen un réseau d'automates temporisés qui a le même comportement distribué.Nous nous intéressons ensuite aux horloges partagées dans lesréseaux d'automates temporisés. Les horloges partagées sont problématiqueslorsque l'on envisage d'implanter ces modèles sur des architecturesdistribuées. Nous montrons comment se passer des horloges partagées, touten préservant le comportement distribué, lorsque cela est possible.Dans la seconde partie, nous nous attachons à formaliser les dépendancesentre les événements dans les représentations en ordre partieldes exécutions des réseaux de Petri (temporels ou non).Les réseaux d'occurrence sont une de ces représentations, et leur structuredonne directement les relations de causalité, conflit et concurrence entreles événements. Cependant, nous montrons que, même dans le cas non temporisé,certaines relations logiques entre les événements nepeuvent pas être directement décrites par ces relations structurelles.Après avoir formalisé les relations logiques en question, nous résolvons leproblème de synthèse suivant: étant donnée une formule logique qui décrit unensemble d'exécutions, construire un réseau d'occurrence associé,quand celui-ci existe.Nous étudions ensuite les relations logiques dans un cadre temporisé simplifié,et montrons que le temps crée des dépendances complexes entre les événements.Ces dépendances peuvent être utilisées pour définir des dépliages canoniques deréseaux de Petri temporels, dans ce cadre simplifié

Avoiding Shared Clocks in Networks of Timed Automata

Networks of timed automata (NTA) are widely used to model distributed real-time systems. Quite often in the literature, the automata are allowed to share clocks, i.e. transitions of one automaton may be guarded by conditions on the value of clocks reset by another automaton. This is a problem when one considers implementing such model in a distributed architecture, since reading clocks a priori requires communications which are not explicitly described in the model. We focus on the following question: given an NTA A1 || A2 where A2 reads some clocks reset by A1, does there exist an NTA A'1 || A'2 without shared clocks with the same behavior as the initial NTA? For this, we allow the automata to exchange information during synchronizations only, in particular by copying the value of their neighbor's clocks. We discuss a formalization of the problem and define an appropriate behavioural equivalence. Then we give a criterion using the notion of contextual timed transition system, which represents the behavior of A2 when in parallel with A1. Finally, we effectively build A'1 || A'2 when it exists

Building Occurrence Nets from Reveals Relations

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A Concurrency-Preserving Translation from Time Petri Nets to Networks of Timed Automata

Real-time distributed systems may be modeled in different formalisms such as time Petri nets (TPN) and networks of timed automata (NTA). This paper focuses on translating a 1-bounded TPN into an NTA and considers an equivalence which takes the distribution of actions into account. This translation is extensible to bounded TPNs. We first use S-invariants to decompose the net into components that give the structure of the automata, then we add clocks to provide the timing information. Although we have to use an extended syntax in the timed automata, this is a novel approach since the other transformations and comparisons of these models did not consider the preservation of concurrency

Building tight occurrence nets from reveals relations

Occurrence nets are a well known partial order model for the concurrent behavior of Petri nets. The causality and conflict relations between events, which are explicitly represented in occurrence nets, induce logical dependencies between event occurrences: the occurrence of an event e in a run implies that all its causal predecessors also occur, and that no event in conflict with e occurs. But these structural relations do not express all the logical dependencies between event occurrences in maximal runs: in particular, the occurrence of e in any maximal run may imply the occurrence of another event that is not a causal predecessor of e, in that run. The reveals relation has been introduced in [1] to express this dependency between two events. Here we generalize the reveals relation to express more general dependencies, involving more than two events, and we introduce ERL logic to express them as boolean formulas. Finally we answer the synthesis problem that arises: given an ERL formula ϕ, is there an occurrence net N such that ϕ describes exactly the dependencies between the events of N