A Forward Reachability Algorithm for Bounded Timed-Arc Petri Nets

Timed-arc Petri nets (TAPN) are a well-known time extension of the Petri net model and several translations to networks of timed automata have been proposed for this model. We present a direct, DBM-based algorithm for forward reachability analysis of bounded TAPNs extended with transport arcs, inhibitor arcs and age invariants. We also give a complete proof of its correctness, including reduction techniques based on symmetries and extrapolation. Finally, we augment the algorithm with a novel state-space reduction technique introducing a monotonic ordering on markings and prove its soundness even in the presence of monotonicity-breaking features like age invariants and inhibitor arcs. We implement the algorithm within the model-checker TAPAAL and the experimental results document an encouraging performance compared to verification approaches that translate TAPN models to UPPAAL timed automata.Comment: In Proceedings SSV 2012, arXiv:1211.587

Two Algebraic Process Semantics for Contextual Nets

We show that the so-called 'Petri nets are monoids' approach initiated by Meseguer and Montanari can be extended from ordinary place/transition Petri nets to contextual nets by considering suitable non-free monoids of places. The algebraic characterizations of net concurrent computations we provide cover both the collective and the individual token philosophy, uniformly along the two interpretations, and coincide with the classical proposals for place/transition Petri nets in the absence of read-arcs

Approximating Petri Net Reachability Along Context-free Traces

We investigate the problem asking whether the intersection of a context-free language (CFL) and a Petri net language (PNL) is empty. Our contribution to solve this long-standing problem which relates, for instance, to the reachability analysis of recursive programs over unbounded data domain, is to identify a class of CFLs called the finite-index CFLs for which the problem is decidable. The k-index approximation of a CFL can be obtained by discarding all the words that cannot be derived within a budget k on the number of occurrences of non-terminals. A finite-index CFL is thus a CFL which coincides with its k-index approximation for some k. We decide whether the intersection of a finite-index CFL and a PNL is empty by reducing it to the reachability problem of Petri nets with weak inhibitor arcs, a class of systems with infinitely many states for which reachability is known to be decidable. Conversely, we show that the reachability problem for a Petri net with weak inhibitor arcs reduces to the emptiness problem of a finite-index CFL intersected with a PNL.Comment: 16 page

Membrane Systems and Petri Net Synthesis

Automated synthesis from behavioural specifications is an attractive and powerful way of constructing concurrent systems. Here we focus on the problem of synthesising a membrane system from a behavioural specification given in the form of a transition system which specifies the desired state space of the system to be constructed. We demonstrate how a Petri net solution to this problem, based on the notion of region of a transition system, yields a method of automated synthesis of membrane systems from state spaces.Comment: In Proceedings MeCBIC 2012, arXiv:1211.347

Automating the transformation-based analysis of visual languages

The final publication is available at Springer via http://dx.doi.org/10.1007/s00165-009-0114-yWe present a novel approach for the automatic generation of model-to-model transformations given a description of the operational semantics of the source language in the form of graph transformation rules. The approach is geared to the generation of transformations from Domain-Specific Visual Languages (DSVLs) into semantic domains with an explicit notion of transition, like for example Petri nets. The generated transformation is expressed in the form of operational triple graph grammar rules that transform the static information (initial model) and the dynamics (source rules and their execution control structure). We illustrate these techniques with a DSVL in the domain of production systems, for which we generate a transformation into Petri nets. We also tackle the description of timing aspects in graph transformation rules, and its analysis through their automatic translation into Time Petri netsWork sponsored by the Spanish Ministry of Science and Innovation, project METEORIC (TIN2008-02081/TIN) and by the Canadian Natural Sciences and Engineering Research Council (NSERC)

Mapping RT-LOTOS specifications into Time Petri Nets

RT-LOTOS is a timed process algebra which enables compact and abstract specification of real-time systems. This paper proposes and illustrates a structural translation of RT-LOTOS terms into behaviorally equivalent (timed bisimilar) finite Time Petri nets. It is therefore possible to apply Time Petri nets verification techniques to the profit of RT-LOTOS. Our approach has been implemented in RTL2TPN, a prototype tool which takes as input an RT-LOTOS specification and outputs a TPN. The latter is verified using TINA, a TPN analyzer developed by LAAS-CNRS. The toolkit made of RTL2TPN and TINA has been positively benchmarked against previously developed RT-LOTOS verification tool

Soundness of workflow nets : classification, decidability, and analysis

Workflow nets, a particular class of Petri nets, have become one of the standard ways to model and analyze workflows. Typically, they are used as an abstraction of the workflow that is used to check the so-called soundness property. This property guarantees the absence of livelocks, deadlocks, and other anomalies that can be detected without domain knowledge. Several authors have proposed alternative notions of soundness and have suggested to use more expressive languages, e.g., models with cancellations or priorities. This paper provides an overview of the different notions of soundness and investigates these in the presence of different extensions of workflow nets. We will show that the eight soundness notions described in the literature are decidable for workflow nets. However, most extensions will make all of these notions undecidable. These new results show the theoretical limits of workflow verification. Moreover, we discuss some of the analysis approaches described in the literature