Modeling concurrency in parallel debugging
PPOPP '90 Proceedings of the second ACM SIGPLAN symposium on Principles & practice of parallel programming
The Complexity of the Finite Containment Problem for Petri Nets
Journal of the ACM (JACM)
ACM Computing Surveys (CSUR)
The home marking problem and some related concepts
Acta Cybernetica
Discrete-Event Simulation of Fluid Stochastic Petri Nets
IEEE Transactions on Software Engineering
An algorithm for the general Petri net reachability problem
STOC '81 Proceedings of the thirteenth annual ACM symposium on Theory of computing
Design and verification of communication procedures: A bottom-up approach
ICSE '78 Proceedings of the 3rd international conference on Software engineering
Expressiveness of Petri Nets with Stopwatches. Dense-time Part
Fundamenta Informaticae
The downward-closure of petri net languages
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming: Part II
Algorithmic verification of asynchronous programs
ACM Transactions on Programming Languages and Systems (TOPLAS)
Expressiveness of Petri Nets with Stopwatches. Dense-time Part
Fundamenta Informaticae
On the Termination of Integer Loops
ACM Transactions on Programming Languages and Systems (TOPLAS)
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An understanding of the mathematical properties of Petri Nets is essential when one wishes to use Petri Nets as an abstract model for concurrent systems. The decidability of various problems which arise in this context is an important aspect of this question. The fact that these problems also arise in the context of other mathematical theories, such as commutative semigroups, closure under linear relations, Matrix Context-Free grammars, or Weak Counter Automata, provides further motivation. The Reachability Problem for Vector Addition Systems - whose decidability is still an open question - is of central importance. We show that a number of Petri Net problems are recursively equivalent to this problem. These include the Liveness Problem (e.g. can a system reach a deadlocked state?), the persistence problem (can a given transition ever be disabled by the firing of another transition?), and the membership and emptiness problems for certain classes of languages generated by Petri Nets. The power of the unrestricted Petri Net model is illustrated by various undecidable equivalence results. In particular, we show that the equality of Reachability Sets and the equivalence of two Petri Nets in terms of their language-generating capability are recursive undecidable. It is hoped that the constructions used to prove our results will shed some light on the source of the complexities of the unrestricted Petri Net model, and may eventually permit us to achieve an optimal balance between representational transparency and analytical power of the Petri Net model.