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Coverability, Termination, and Finiteness in Recursive Petri Nets

Finkel Alaina, Haddad Sergeb, Khmelnitsky Igor

Fundamenta Informaticae

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2021

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Vol. 183, nr 1-2

33--66

EN

In the early two-thousands, Recursive Petri nets have been introduced in order to model distributed planning of multi-agent systems for which counters and recursivity were necessary. Although Recursive Petri nets strictly extend Petri nets and context-free grammars, most of the usual problems (reachability, coverability, finiteness, boundedness and termination) were known to be solvable by using non-primitive recursive algorithms. For almost all other extended Petri nets models containing a stack, the complexity of coverability and termination are unknown or strictly larger than EXPSPACE. In contrast, we establish here that for Recursive Petri nets, the coverability, termination, boundedness and finiteness problems are EXPSPACE-complete as for Petri nets. From an expressiveness point of view, we show that coverability languages of Recursive Petri nets strictly include the union of coverability languages of Petri nets and context-free languages. Thus we get a more powerful model than Petri net for free.

2

SMC4AC : A New Symbolic Model Checker for Intelligent Agent Communication

El Kholy W., Bentahar J., Qu H., El Menshawy M., Dssouli R.

Fundamenta Informaticae

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2017

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Vol. 152, nr 3

223--271

EN

Social approaches have been put forward to define semantics for intelligent agent communication messages and to tackle the shortcomings of mental approaches. Formal semantics of those social approaches can be model checked as they are focused on public behaviors instead of private mental states. Social conditional commitments are essential concepts in social approaches that can effectively model agent communications. However, conditional commitments exclusively are not able to model agent communication actions, the cornerstone of the fundamental agent communication theory, namely speech act theory. These actions provide mechanisms for dynamic interactions and enable designers to track the evolution of active conditional commitments. From the perspective of model checking, we need to define a formal and computationally grounded semantics for relevant social actions that can directly be applied to active conditional commitments. This manuscript describes a new symbolic model checker, SMC4AC, developed and implemented to automate the verification of interaction among intelligent agents. SMC4AC is the result of developing a new symbolic model checking algorithm devoted to CTLCα, a combination of CTL and new temporal modalities to represent and reason about conditional commitments and common commitment actions. The core of this paper consists of a new logical language, a detailed description of the symbolic algorithms needed for commitments and their action modalities, complexity analysis, implementation and application. The implementation of our algorithm and its graphical user interface is built on top of the MCMAS symbolic model checker tailored for checking intelligent multi-agent systems. We select business processes and multi-agent interaction protocols as application domains to test and validate the effectiveness and scalability of SMC4AC. We report extensive experimental results, which confirm the theoretical findings and make SMC4AC practical.

3

Expressiveness of Petri Nets with Stopwatches. Discrete-time Part

Magnin M, Molinaro P., Roux O-H.

Fundamenta Informaticae

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2009

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Vol. 97, nr 1/2

139-176

EN

With this contribution, we aim to draw a comprehensive classification of Petri nets with stopwatches w.r.t. expressiveness and decidability issues. This topic is too ambitious to be summarized in a single paper. That is why we present our results in two different parts. In the first part of our work, we established new results regarding to both dense-time and discrete-time semantics. We now focus on the discrete-time specificities. We address the class of bounded Petri nets with stopwatches and reset arcs (rSwPNs), which is an extension of T-time Petri nets (TPNs) where time is associated with transitions. Stopwatches can be reset, stopped and started. We recall the formal dense-time and discrete-time semantics of these models in terms of Transition Systems. We study the expressiveness of rSwPNs and its subclasses w.r.t. (weak) bisimilarity (behavioral semantics). The main results are following: 1) Discrete-time bounded TPNs, discrete-time bounded rSwPNs and untimed Petri nets are equally expressive; 2) The resulting (final) classification of models is given by a set of relations explained in Fig. 7. While investigating expressiveness, we exhibit proofs that can be easily extended to the resolution of decidability issues. Among other results, we prove that, for bounded rSwPNs, the state and marking reachability problems - undecidable with dense-time semantics - are decidable when discrete-time is considered. Table 1 gives a synthesis of the main decidability results for these models. For the sake of simplicity, our results are explained on a model such that the stopwatches behaviors are expressed using inhibitor arcs. Our conclusions can however be easily extended to the general class of Stopwatch Petri nets.

4

Expressiveness of Petri Nets with Stopwatches. Dense-time Part

Magnin M, Molinaro P., Roux O-H.

Fundamenta Informaticae

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2009

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Vol. 97, nr 1/2

111-138

EN

With this contribution, we aim to draw a comprehensive classification of Petri nets with stopwatches w.r.t. expressiveness and decidability issues. This topic is too ambitious to be summarized in a single paper. That is why we present our results in two different parts. The scope of this first paper is to address the general results that apply for both dense-time and discrete-time semantics. We study the class of bounded Petri nets with stopwatches and reset arcs (rSwPNs), which is an extension of T-time Petri nets (TPNs) where time is associated with transitions. Stopwatches can be reset, stopped and started. We give the formal dense-time and discrete-time semantics of these models in terms of Transition Systems. We study the expressiveness of rSwPNs and its subclasses w.r.t. (weak) bisimilarity (behavioral semantics). The main results are following: 1) bounded rSw- PNs and 1-safe rSwPNs are equally expressive; 2) For all models, reset arcs add expressiveness. 3) The resulting partial classification of models is given by a set of relations explained in Fig. 7: in the forthcoming paper, we will complete these results by covering expressiveness and decidability issues when discrete-time nets are considered. For the sake of simplicity, our results are explained on a model such that the stopwatches behaviors are expressed using inhibitor arcs. Our conclusions can however be easily extended to the general class of Stopwatch Petri nets.

5

Timed Cooperating Automata

Lanotte R., Maggiolo-Schettini A.

Fundamenta Informaticae

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2000

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Vol. 43, Nr 1-4

153-173

EN

We propose Timed Cooperating Automata (TC As), an extension of the model Cooperating Automata of Harel and Drusinsky, and we investigate some basic properties. In particular we consider variants of TCAs based on the presence or absence of internal activity, urgency and reactivity, and we compare the expressiveness of these variants with that of the classical model of Timed Automata (TAs) and its extensions with periodic clock constraints and with silent moves. We consider also closure and decidability properties of TCAs and start a study on succinctness of their variants with respect to that of TAs.