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1

On Deadlockability, Liveness and Reversibility in Subclasses of Weighted Petri Nets

Hujsa T., Devillers R.

Fundamenta Informaticae

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2018

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Vol. 161, nr 4

383--421

EN

Liveness, (non-)deadlockability and reversibility are behavioral properties of Petri nets that are fundamental for many real-world systems. Such properties are often required to be monotonic, meaning preserved upon any increase of the marking. However, their checking is intractable in general and their monotonicity is not always satisfied. To simplify the analysis of these features, structural approaches have been fruitfully exploited in particular subclasses of Petri nets, deriving the behavior from the underlying graph and the initial marking only, often in polynomial time. In this paper, we further develop these efficient structural methods to analyze deadlockability, liveness, reversibility and their monotonicity in weighted Petri nets. We focus on the join-free subclass, which forbids synchronizations, and on the homogeneous asymmetric-choice subclass, which allows conflicts and synchronizations in a restricted fashion. For the join-free nets, we provide several structural conditions for checking liveness, (non-)deadlockability, reversibility and their monotonicity. Some of these methods operate in polynomial time. Furthermore, in this class, we show that liveness, non-deadlockability and reversibility, taken together or separately, are not always monotonic, even under the assumptions of structural boundedness and structural liveness. These facts delineate more sharply the frontier between monotonicity and non-monotonicity of the behavior in weighted Petri nets, present already in the join-free subclass. In addition, we use part of this new material to correct a flaw in the proof of a previous characterization of monotonic liveness and boundedness for homogeneous asymmetric-choice nets, published in 2004 and left unnoticed.

2

Synthesis of Live and Bounded Persistent Systems

Best E., Devillers R.

Fundamenta Informaticae

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2015

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Vol. 140, nr 1

39--59

EN

This paper presents a dedicated Petri net synthesis algorithm for the case that a transition system is finite, live, and persistent. In particular, the paper delineates exactly when and how a structurally persistent net may be constructed, by crystallising, out of a general region-theoretic approach, a minimised set of simplified systems of linear inequalities. This extends previous results where reversibility, instead of liveness, played an important role.

3

A Petri Net Interpretation of Open Reconfigurable Systems

Peschanski F., Klaudel H., Devillers R.

Fundamenta Informaticae

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2013

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Vol. 122, nr 1-2

85--117

EN

We present a Petri net interpretation of the pi-graphs - a graphical variant of the picalculus where recursion and replication are replaced by iteration. The concise and syntax-driven translation can be used to reason in Petri net terms about open reconfigurable systems. We demonstrate that the pi-graphs and their translated high-level Petri nets agree at the semantic level. In consequence, existing results on pi-graphs naturally extend to the translated Petri nets, most notably a guarantee of finiteness by construction.

4

Petri Net Semantics of the Finite p-calculus Terms

Devillers R., Klaudel H., Koutny M.

Fundamenta Informaticae

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2006

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Vol. 70, nr 3

203-226

EN

In this paper we propose a translation into high level Petri nets of the terms of a finite fragment of the p-calculus. Our construction renders in a compositional way the control flow aspects present in p-calculus process expressions, by adapting the existing graph-theoretic net composition operators. Those aspects which are related to term rewriting, as well as name binding, are handled through special inscriptions of places, transitions and arcs, together with a suitable choice of the initial marking.

5

Synchronous and Asynchronous Communications in Composable Parameterized High-Level Petri Nets

Devillers R., Klaudel H.

Fundamenta Informaticae

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2005

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Vol. 66, nr 3

221--257

EN

In the domain of parameterized composable high-level Petri nets (M-nets), we shall combine the refinement, the synchronization and the asynchronous link operations in a unified and general setup, while keeping the expected properties of those operations. In particular, the various high-level net operations are consistent through unfolding with their low-level counterparts, and the usual commutativity and idempotency properties are fulfilled at the syntactic level up to structural equivalences.

6

Asynchronous Box Calculus

Devillers R., Klaudel H., Koutny M., Pommereau F.

Fundamenta Informaticae

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2003

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Vol. 54, nr 4

295-344

EN

The starting point of this paper is an algebraic Petri net framework allowing one to express net compositions, such as iteration and parallel composition, as well as transition synchronisation and restriction. We enrich the original model by introducing new constructs supporting asynchronous interprocess communication. Such a communication is made possible thanks to special `buffer' places where different transitions (processes) may deposit and remove tokens. We also provide an abstraction mechanism, which hides buffer places, effectively making them private to the processes communicating through them. We then provide an algebra of process expressions, whose constants and operators directly correspond to those used in the Petri net framework. Such a correspondence is used to associate nets to process expressions in a compositional way. That the resulting algebra of expressions is consistent with the net algebra is demonstrated by showing that an expression and the corresponding net generate isomorphic transition systems. This results in the Asynchronous Box Calculus (or ABC), which is a coherent dual model, based on Petri nets and process expressions, suitable for modelling and analysing distributed systems whose components can interact using both synchronous and asynchronous communication.

7

General response time computation for the deadline driven scheduling of periodic tasks

Devillers R., Goossens J.

Fundamenta Informaticae

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1999

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Vol. 40, Nr 2,3

199-219

EN

In this paper we study the problem of scheduling hard real-time periodic task sets with a dynamic and preemptive scheduler. We will focus on the response time notion, its interest and its effective computation for the deadline driven scheduler. We present a general calculation procedure for determining the response time of the kth request of a task in asynchronous systems with general as well as arbitrary deadlines. Finally, we analyze the performance of the computation so defined, both in terms of time and memory requirements.