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Modeling Multivalued Genetic Regulatory Networks Using HighLevel Petri Nets
 In: G. Ciardo and P. Darondeau (eds), Proc. of the Int. Conf. on the Application and Theory of Petri Nets, Lecture Notes in Computer Science 3536
, 2005
"... Abstract. Regulatory networks are at the core of all biological functions from biochemical pathways to gene regulation and cell communication processes. Because of the complexity of the interweaving retroactions, the overall behavior is difficult to grasp and the development of formal methods is ne ..."
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Abstract. Regulatory networks are at the core of all biological functions from biochemical pathways to gene regulation and cell communication processes. Because of the complexity of the interweaving retroactions, the overall behavior is difficult to grasp and the development of formal methods is needed in order to confront the supposed properties of the biological system to the model. We revisit here the tremendous work of R. Thomas and show that its binary and also its multivalued approach can be expressed in a unified way with highlevel Petri nets. A compact modeling of genetic networks is proposed in which the tokens represent gene’s expression levels and their dynamical behavior depends on a certain number of biological parameters. This allows us to take advantage of techniques and tools in the field of highlevel Petri nets. A developed prototype lets a biologist to verify systematically the coherence of the system under various hypotheses. These hypotheses are translated into temporal logic formulae and the modelchecking techniques are used to retain only the models whose behavior is coherent with the biological knowledge. 1
Merged Processes  a New Condensed Representation of Petri Net Behaviour
, 2005
"... Model checking based on Petri net unfoldings is an approach widely applied to cope with the state space explosion problem. In this paper we propose a new condensed representation of a Petri net’s behaviour called merged processes, which copes well not only with concurrency, but also with the other s ..."
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Model checking based on Petri net unfoldings is an approach widely applied to cope with the state space explosion problem. In this paper we propose a new condensed representation of a Petri net’s behaviour called merged processes, which copes well not only with concurrency, but also with the other sources of state space explosion, viz. sequences of choices and nonsafeness. Moreover, this representation is sufficiently similar to the traditional unfoldings, so that a large body of results developed for the latter can be reused. Experimental results indicate that the proposed representation of a Petri net’s behaviour alleviates the state space explosion problem to a significant degree and is suitable for model checking.
Detecting State Coding Conflicts in STG Unfoldings Using SAT
 IN PROC. OF THE 4TH INT. CONF. ON APPLICATION OF CONCURRENCY TO SYSTEM DESIGN
"... The behaviour of asynchronous circuits is often described by Signal Transition Graphs (STGs), which are Petri nets whose transitions are interpreted as rising and falling edges of signals. One of the crucial problems in the synthesis of such circuits is that of identifying whether an STG satisfies t ..."
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Cited by 13 (9 self)
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The behaviour of asynchronous circuits is often described by Signal Transition Graphs (STGs), which are Petri nets whose transitions are interpreted as rising and falling edges of signals. One of the crucial problems in the synthesis of such circuits is that of identifying whether an STG satisfies the Complete State Coding (CSC) requirement, e.g., by using model checking based on the state graph of an STG. In
Directed unfolding of petri nets
 the Workshop on Unfolding and PartialOrder Techniques (UFO07
, 2007
"... Abstract. The key to efficient onthefly reachability analysis based on unfolding is to focus the expansion of the finite prefix towards the desired marking. However, current unfolding strategies typically equate to blind (breadthfirst) search. They do not exploit the knowledge of the marking that ..."
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Abstract. The key to efficient onthefly reachability analysis based on unfolding is to focus the expansion of the finite prefix towards the desired marking. However, current unfolding strategies typically equate to blind (breadthfirst) search. They do not exploit the knowledge of the marking that is sought, merely entertaining the hope that the road to it will be short. This paper investigates directed unfolding, which exploits problemspecific information in the form of a heuristic function to guide the unfolding towards the desired marking. In the unfolding context, heuristic values are estimates of the distance between configurations. We show that suitable heuristics can be automatically extracted from the original net. We prove that unfolding can rely on heuristic search strategies while preserving the finiteness and completeness of the generated prefix, and in some cases, the optimality of the firing sequence produced. We also establish that the size of the prefix obtained with a useful class of heuristics is never worse than that obtained by blind unfolding. Experimental results demonstrate that directed unfolding scales up to problems that were previously out of reach of the unfolding technique. 1
Causal Time Calculus
 In Proc. FORMATS’03, LNCS
, 2002
"... Abstract. We present a process algebra suitable to the modelling of timed concurrent systems and to their efficient verification through model checking. The algebra is provided with two consistent semantics: a structural operational semantics (as usual for process algebras) and a denotational semant ..."
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Abstract. We present a process algebra suitable to the modelling of timed concurrent systems and to their efficient verification through model checking. The algebra is provided with two consistent semantics: a structural operational semantics (as usual for process algebras) and a denotational semantics in terms of Petri nets in which time is introduced through counters of explicit clock ticks. This way of modelling time has been called causal time so the process algebra is itself called the Causal Time Calculus (CTC). It was shown in a separate paper [3] that the causal time approach allowed for efficient verification but suffered from a sensitivity to the constants to which counts of ticks are compared. We show in this paper how this weakness can be removed. 1
Computing the Reveals Relation in Occurrence Nets
, 2011
"... Topics: Petri net unfoldings are a useful tool to tackle statespace explosion in verification and related tasks. Moreover, their structure allows to access directly the relations of causal precedence, concurrency, and conflict between events. Here, we explore the data structure further, to determin ..."
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Topics: Petri net unfoldings are a useful tool to tackle statespace explosion in verification and related tasks. Moreover, their structure allows to access directly the relations of causal precedence, concurrency, and conflict between events. Here, we explore the data structure further, to determine the following relation: event a is said to reveal event b iff the occurrence of a implies that b inevitably occurs, too, be it before, after, or concurrently with a. Knowledge of reveals facilitates in particular the analysis of partially observable systems, in the context of diagnosis, testing, or verification; it can also be used to generate more concise representations of behaviours via abstractions. The reveals relation was previously introduced in the context of fault diagnosis, where it was shown that the reveals relation was decidable: for a given pair a,b in the unfolding U of a safe Petri net N, a finite prefix P of U is sufficient to decide whether or not a reveals b. In this paper, we first considerably improve the bound on P. We then show that there exists an efficient algorithm for computing the relation on a given prefix. We have implemented the algorithm and report on experiments. Structure and behaviour of Petri Nets; partialorder theory of concurrency; automatic analysis 1
Combining Symbolic and Partial Order Methods for Model Checking 1Safe Petri Nets
, 2002
"... In this work, methods are presented for model checking finite state asynchronous systems, more specifically 1safe Petri nets, with the aim of alleviating the state explosion problem. Symbolic model checking techniques are used, combined with two partial order semantics known as net unfoldings and p ..."
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In this work, methods are presented for model checking finite state asynchronous systems, more specifically 1safe Petri nets, with the aim of alleviating the state explosion problem. Symbolic model checking techniques are used, combined with two partial order semantics known as net unfoldings and processes. We start
Logic Synthesis Avoiding State Space Explosion
"... The behaviour of asynchronous circuits is often described by Signal Transition Graphs (STGs), which are Petri nets whose transitions are interpreted as rising and falling edges of signals. One of the crucial problems in the synthesis of such circuits is deriving equations for logic gates implemen ..."
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Cited by 2 (1 self)
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The behaviour of asynchronous circuits is often described by Signal Transition Graphs (STGs), which are Petri nets whose transitions are interpreted as rising and falling edges of signals. One of the crucial problems in the synthesis of such circuits is deriving equations for logic gates implementing each output signal of the circuit. This is usually done using reachability graphs.
Reachability via Compositionality in Petri nets
"... Abstract. We introduce a novel technique for checking reachability in Petri nets that relies on a recently introduced compositional algebra of nets. We prove that the technique is correct, and discuss our implementation. We report promising experimental results on some wellknown examples. ..."
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Abstract. We introduce a novel technique for checking reachability in Petri nets that relies on a recently introduced compositional algebra of nets. We prove that the technique is correct, and discuss our implementation. We report promising experimental results on some wellknown examples.