: We survey 25 years of research on decidability issues for Petri nets. We collect results on the decidability of important properties, equivalence notions, and temporal logics. 1. Introduction Petri nets are one of the most popular formal models for the representation and analysis of parallel processes. They are due to C.A. Petri, who introduced them in his doctoral dissertation in 1962. Some years later, and independently from Petri's work, Karp and Miller introduced vector addition systems [47], a simple mathematical structure which they used to analyse the properties of "parallel program schemata', a model for parallel computation. In their seminal paper on parallel program schemata, Karp and Miller studied some decidability issues for vector addition systems, and the topic continued to be investigated by other researchers. When Petri's ideas reached the States around 1970, it was observed that Petri nets and vector addition systems were mathematically equivalent, even though thei...

We study Petri nets with Reset arcs (also Transfer and Doubling arcs) in combination with other extensions of the basic Petri net model. While Reachability is undecidable in all these extensions (indeed they are Turing-powerful), we exhibit unexpected frontiers for the decidability of Termination, Coverability, Boundedness and place-Boundedness. In particular, we show counter-intuitive separations between seemingly related problems. Our main theorem is the very surprising fact that boundedness is undecidable for Petri nets with Reset arcs.

The growing popularity of multi-threading has led to a great number of software libraries that support access by multiple threads. We present Local/Global Finite State Machines (LGFSMs) as a model for a certain class of multithreaded libraries. We have developed a tool called Beacon that does parameterized model checking of LGFSMs. We demonstrate the expressiveness of LGFSMs as models, and the effectiveness of Beacon as a model checking tool by (1) modeling a multithreaded memory manager Rockall developed at Microsoft Research as an LGFSM, and (2) using Beacon to check a critical safety property of Rockall.

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Abstract. We study data nets, a generalisation of Petri nets in which tokens carry data from linearly-ordered infinite domains and in which whole-place operations such as resets and transfers are possible. Data nets subsume several known classes of infinite-state systems, including multiset rewriting systems and polymorphic systems with arrays. We show that coverability and termination are decidable for arbitrary data nets, and that boundedness is decidable for data nets in which whole-place operations are restricted to transfers. By providing an encoding of lossy channel systems into data nets without whole-place operations, we establish that coverability, termination and boundedness for the latter class have non-primitive recursive complexity. The main result of the paper is that, even for unordered data domains (i.e., with only the equality predicate), each of the three verification problems for data nets without whole-place operations has non-elementary complexity. 1

We examine both the modeling power of normal and sinkless Petri nets and the computational complexities of various classical decision problems with respect to these two classes. We argue that although neither normal nor sinkless Petri nets are strictly more powerful than persistent Petri nets, they nonetheless are both capable of modeling a more interesting class of problems. On the other hand, we give strong evidence that normal and sinkless Petri nets are easier to analyze than persistent Petri nets. In so doing, we apply techniques originally developed for conflict-free Petri nets --- a class defined solely in terms of the structure of the the net --- to sinkless Petri nets --- a class defined in terms of the behavior of the net. As a result, we give the first comprehensive complexity analysis of a class of potentially unbounded Petri nets defined in terms of their behavior. 1 Introduction Many aspects of the fundamental nature of computation are often studied via formal m...

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Component-Based Software Engineering focuses on the reuse of existing software components. In practice, most components cannot be integrated directly into an application-to-be, because they are incompatible. Software Adaptation aims at generating, as automatically as possible, adaptors to compensate mismatch between component interfaces, and is therefore a promising solution for the development of a real market of components promoting software reuse. In this article, we present our approach for software adaptation which relies on an abstract notation based on synchronous vectors and transition systems for governing adaptation rules. Our proposal is supported by dedicated algorithms that generate automatically adaptor protocols. These algorithms have been implemented in a tool, called Adaptor, that can be used through a user-friendly graphical interface.

We study the complexity of model-checking Petri Nets w.r.t. the propositional linear-time -calculus. Esparza has shown in [5] that it is decidable, but the space complexity of his algorithm is exponential in the size of the system and double exponential in the size of the formula. In this paper we show that the complexity in the size of the formula can be reduced to polynomial space. We also prove that this is the best one can do. We also show that for the subclass of BPPs the problem has already the same complexity as for arbitrary nets. Furthermore we obtain the same results for the linear time temporal logic LTL, which is strictly less expressive than the linear-time -calculus. 1 Introduction There is now a well established theory for automatic verification of finite state concurrent systems. Recently, the problem of extending this theory to infinite state systems has been addressed. There are mainly two different directions for the automatic verification of infinite state systems...

The covering and boundedness problems for branching vector addition systems are