arXiv subjects

Raymond Devillers

Publications and source records attributed to Raymond Devillers.

12 recordsLinked to original sources

arXiv2026

Well-Formed Free-Choice Petri Nets Revisited

The theory of free-choice Petri nets is an established field, initiated in the 1970s by F. Commoner and M. Hack. We revisit well-formed free-choice nets (those admitting markings that are both live and bounded) and provide a new characterisation by introducing semi-T-components. This notion is dual to that of semi-S-components, which in turn correspond to the well-known minimal siphons. By highlighting the symmetry between these dual concepts, we derive the classical coverability theorems for T- and S-components, as well as the duality theorem---stating that a free-choice net is well-formed if and only if its reverse-dual is also well-formed---using highly symmetric arguments.

cs.FL↗

arXiv2026

Persistent Permutability in Choice Petri Nets

Persistence is a strong, global, behavioural property of a Petri net, meaning that no activity can disable a different activity. Persistent permutability is a weaker property, pertaining to individual interleavings of a Petri net and stating that a non-persistent sequence can be permuted into a persistent one. We identify Petri net classes for which persistent permutability already suffices to imply overall persistence. These classes generalise free-choice nets and are related to Petri's concept of ``confusion'', while they are distinguished from each other by diverse restrictions on the choice structure of a net. We prove Ochmanski's conjecture to be correct for these classes.

cs.FL↗

arXiv2022

On the Complexity of Techniques That Make Transition Systems Implementable by Boolean Nets

Synthesis consists in deciding whether a given labeled transition system (TS) $A$ can be implemented by a net $N$ of type $\tau$. In case of a negative decision, it may be possible to convert $A$ into an implementable TS $B$ by applying various modification techniques, like relabeling edges that previously had the same label, suppressing edges/states/events, etc. It may however be useful to limit the number of such modifications to stay close to the original problem, or optimize the technique. In this paper, we show that most of the corresponding problems are NP-complete if $\tau$ corresponds to the type of flip-flop nets or some flip-flop net derivatives.

cs.CC↗

arXiv2021

Some Basic Techniques allowing Petri Net Synthesis: Complexity and Algorithmic Issues

In Petri net synthesis we ask whether a given transition system $A$ can be implemented by a Petri net $N$. Depending on the level of accuracy, there are three ways how $N$ can implement $A$: an embedding, the least accurate implementation, preserves only the diversity of states of $A$; a language simulation already preserves exactly the language of $A$; a realization, the most accurate implementation, realizes the behavior of $A$ exactly. However, whatever the sought implementation, a corresponding net does not always exist. In this case, it was suggested to modify the input behavior -- of course as little as possible. Since transition systems consist of states, events and edges, these components appear as a natural choice for modifications. In this paper we show that the task of converting an unimplementable transition system into an implementable one by removing as few states or events or edges as possible is NP-complete -- regardless of what type of implementation we are aiming for; we also show that the corresponding parameterized problems are $W[2]$-hard, where the number of removed components is considered as the parameter; finally, we show there is no $c$-approximation algorithm (with a polynomial running time) for neither of these problems, for every constant $c\geq 1$.

cs.FL↗

arXiv2021

Synthesis of Pure and Impure Petri nets With Restricted Place-environments: Complexity Issues

Petri net synthesis consists in deciding for a given transition system $A$ whether there exists a Petri net $N$ whose reachability graph is isomorphic to $A$. Several works examined the synthesis of Petri net subclasses that restrict, for every place $p$ of the net, the cardinality of its preset or of its postset or both in advance by small natural numbers $\varrho$ and $\kappa$, respectively, such as for example (weighted) marked graphs, (weighted) T-systems and choice-free nets. In this paper, we study the synthesis aiming at Petri nets which have such restricted place environments, from the viewpoint of classical and parameterized complexity: We first show that, for any fixed natural numbers $\varrho$ and $\kappa$, deciding whether for a given transition system $A$ there is a Petri net $N$ such that (1) its reachability graph is isomorphic to $A$ and (2) for every place $p$ of $N$ the preset of $p$ has at most $\varrho$ and the postset of $p$ has at most $\kappa$ elements is doable in polynomial time. Secondly, we introduce a modified version of the problem, namely Environment Restricted Synthesis (ERS, for short), where $\varrho$ and $\kappa$ are part of the input, and show that ERS is NP-complete, regardless whether the sought net is impure or pure. In case of the impure nets, our methods also imply that ERS parameterized by $\varrho+\kappa$ is $W[2]$-hard.

cs.FL↗

arXiv2021

Articulations and Products of Transition Systems and their Applications to Petri Net Synthesis

In order to speed up the synthesis of Petri nets from labelled transition systems, a divide and conquer strategy consists in defining decompositions of labelled transition systems, such that each component is synthesisable iff so is the original system. Then corresponding Petri Net composition operators are searched to combine the solutions of the various components into a solution of the original system. The paper presents two such techniques, which may be combined: products and articulations. They may also be used to structure transition systems, and to analyse the performance of synthesis techniques when applied to such structures.

cs.FL↗

arXiv2019

Dynamic exploration of multi-agent systems with timed periodic tasks

We formalise and study multi-agent timed models MAPTs (Multi-Agent with timed Periodic Tasks), where each agent is associated to a regular timed schema upon which all possibles actions of the agent rely. MAPTs allow for an accelerated semantics and a layered structure of the state space, so that it is possible to explore the latter dynamically and use heuristics to greatly reduce the computation time needed to address reachability problems. We apply MAPTs to explore state spaces of autonomous vehicles and compare it with other approaches in terms of expressivity, abstraction level and computation time.

cs.MA↗

arXiv2019

Efficient Synthesis of Weighted Marked Graphs with Circular Reachability Graph, and Beyond

In previous studies, several methods have been developed to synthesise Petri nets from labelled transition systems (LTS), often with structural constraints on the net and on the LTS. In this paper, we focus on Weighted Marked Graphs (WMGs) and Choice-Free (CF) Petri nets, two weighted subclasses of nets in which each place has at most one output; WMGs have the additional constraint that each place has at most one input. We provide new conditions for checking the existence of a WMG whose reachability graph is isomorphic to a given circular LTS, i.e. forming a single cycle; we develop two new polynomial-time synthesis algorithms dedicated to these constraints: the first one is LTS-based (classical synthesis) while the second one is vector-based (weak synthesis) and more efficient in general. We show that our conditions also apply to CF synthesis in the case of three-letter alphabets, and we discuss the difficulties in extending them to CF synthesis over arbitrary alphabets.

cs.DS↗

arXiv2019

Synthesis of Weighted Marked Graphs from Constrained Labelled Transition Systems: A Geometric Approach

Recent studies investigated the problems of analysing Petri nets and synthesising them from labelled transition systems (LTS) with two labels (transitions) only. In this paper, we extend these works by providing new conditions for the synthesis of Weighted Marked Graphs (WMGs), a well-known and useful class of weighted Petri nets in which each place has at most one input and one output. Some of these new conditions do not restrict the number of labels; the other ones consider up to 3 labels. Additional constraints are investigated: when the LTS is either finite or infinite, and either cyclic or acyclic. We show that one of these conditions, developed for 3 labels, does not extend to 4 nor to 5 labels. Also, we tackle geometrically the WMG-solvability of finite, acyclic LTS with any number of labels.

cs.FL↗

arXiv2015

Indefinite waitings in MIRELA systems

MIRELA is a high-level language and a rapid prototyping framework dedicated to systems where virtual and digital objects coexist in the same environment and interact in real time. Its semantics is given in the form of networks of timed automata, which can be checked using symbolic methods. This paper shows how to detect various kinds of indefinite waitings in the components of such systems. The method is experimented using the PRISM model checker.

cs.SE↗

arXiv2010

A Decidable Characterization of a Graphical Pi-calculus with Iterators

This paper presents the Pi-graphs, a visual paradigm for the modelling and verification of mobile systems. The language is a graphical variant of the Pi-calculus with iterators to express non-terminating behaviors. The operational semantics of Pi-graphs use ground notions of labelled transition and bisimulation, which means standard verification techniques can be applied. We show that bisimilarity is decidable for the proposed semantics, a result obtained thanks to an original notion of causal clock as well as the automatic garbage collection of unused names.

cs.FL↗

arXiv2008

Power-Aware Real-Time Scheduling upon Identical Multiprocessor Platforms

In this paper, we address the power-aware scheduling of sporadic constrained-deadline hard real-time tasks using dynamic voltage scaling upon multiprocessor platforms. We propose two distinct algorithms. Our first algorithm is an off-line speed determination mechanism which provides an identical speed for each processor. That speed guarantees that all deadlines are met if the jobs are scheduled using EDF. The second algorithm is an on-line and adaptive speed adjustment mechanism which reduces the energy consumption while the system is running.

cs.OS↗