Abstract Interleaving Semantics for Reconfigurable Petri Nets

Reconfigurable Petri nets are Petri nets together with rules for the dynamic change of the nets. We employ them for the formal modeling in the context of the Living Place Hamburg, a smart home that is an urban apartment serving as  a laboratory for investigating different areas of ambient intelligence. The interaction of the resident and the smart home is modeled using informal descriptions of scenarios. These scenarios provide the resident's procedures together with the smart home's support. A case study using reconfigurable Petri nets for modeling these scenarios has required extensions of the theory and has clearly shown the need for an interleaving semantics for reconfigurable Petri nets. Scenarios are then given by nets, namely decorated place/transition nets that can be adapted to the evolving subgoals by applying rules that change the nets and hence the behavior of the smart home. Decorated place/transition nets are annotated place/transition nets with additional transition labels that may change when the transition is fired. To obtain such reconfigurable Petri nets  we prove that decorated place/transition nets  give rise to an M-adhesive HLR category. The abstract interleaving semantics we introduce is a graph with nodes that consist of an isomorphism class of the net structure and an isomorphism class of the current  marking. Arcs between these nodes represent computation steps being either a transition firing or a direct transformation

Efficient Reachability Graph Representation of Petri Nets With Unbounded Counters

AbstractIn this paper, we define a class of Petri nets, called Petri nets with counters, that can be seen as place/transition Petri nets enriched with a vector of integer variables on which linear operations may be applied. Their semantics usually leads to huge or infinite reachability graphs. Then, a more compact representation for this semantics is defined as a symbolic state graph whose nodes possibly encode infinitely many values for the variables. Both representations are shown behaviourally equivalent

Efficient reachability graph representation of Petri nets with unbounded counters

International audienceIn this paper, we define a class of Petri nets, called Petri nets with counters, that can be seen as place/transition Petri nets enriched with a vector of integer variables on which linear operations may be applied. Their semantics usually leads to huge or infinite reachability graphs. Then, a more compact representation for this semantics is defined as a symbolic state graph whose nodes possibly encode infinitely many values for the variables. Both representations are shown behaviourally equivalent

From PNML to counter systems for accelerating Petri Nets with FAST

We use the tool FAST to check parameterized safety properties on Petri nets with a large or infinite state space. Although this tool is not dedicated to Petri nets, it can be used for these as place/transition nets (and some of their extensions) are subcases of FASTinput model. The originality of the tool lies in the use of acceleration techniques in order to compute the exact reachability set for infinite systems. In this paper, we present the automatic transformation of Petri nets written in PNML (Petri Net Markup Language) into counter systems. Then, FAST provides a simple but very powerful language to express complex properties and check these

Pomsets and Unfolding of Reset Petri Nets

International audienceReset Petri nets are a particular class of Petri nets where transition firings can remove all tokens from a place without checking if this place actually holds tokens or not. In this paper we look at partial order semantics of such nets. In particular, we propose a pomset bisimulation for comparing their concurrent behaviours. Building on this pomset bisimulation we then propose a generalization of the standard finite complete prefixes of unfolding to the class of safe reset Petri nets

Bisimilarity and Behaviour-Preserving Reconfigurations of Open Petri Nets

We propose a framework for the specification of behaviour-preserving reconfigurations of systems modelled as Petri nets. The framework is based on open nets, a mild generalisation of ordinary Place/Transition nets suited to model open systems which might interact with the surrounding environment and endowed with a colimit-based composition operation. We show that natural notions of bisimilarity over open nets are congruences with respect to the composition operation. The considered behavioural equivalences differ for the choice of the observations, which can be single firings or parallel steps. Additionally, we consider weak forms of such equivalences, arising in the presence of unobservable actions. We also provide an up-to technique for facilitating bisimilarity proofs. The theory is used to identify suitable classes of reconfiguration rules (in the double-pushout approach to rewriting) whose application preserves the observational semantics of the net.Comment: To appear in "Logical Methods in Computer Science", 41 page

From PNML to counter systems for accelerating Petri Nets with FAST

We use the tool FAST to check parameterized safety properties on Petri nets with a large or infinite state space. Although this tool is not dedicated to Petri nets, it can be used for these as place/transition nets (and some of their extensions) are subcases of FASTinput model. The originality of the tool lies in the use of acceleration techniques in order to compute the exact reachability set for infinite systems. In this paper, we present the automatic transformation of Petri nets written in PNML (Petri Net Markup Language) into counter systems. Then, FAST provides a simple but very powerful language to express complex properties and check these