A multiparameter analysis of the boundedness problem for vector addition systems
Journal of Computer and System Sciences
Parametric real-time reasoning
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Normal and sinkless Petri nets
Journal of Computer and System Sciences
Theoretical Computer Science
Timing parameter characterization of real-time systems
CIAA'03 Proceedings of the 8th international conference on Implementation and application of automata
Model checking lossy vector addition systems
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
Complexity analysis of the backward coverability algorithm for VASS
RP'11 Proceedings of the 5th international conference on Reachability problems
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Upward-closed sets of integer vectors enjoy the merit of having a finite number of minimal elements, which is behind the decidability of a number of Petri net related problems. In general, however, such a finite set of minimal elements may not be effectively computable. In this paper, we develop a unified strategy for computing the sizes of the minimal elements of certain upward-closed sets associated with Petri nets. Our approach can be regarded as a refinement of a previous work by Valk and Jantzen (in which a necessary and sufficient condition for effective computability of the set was given), in the sense that complexity bounds now become available provided that a bound can be placed on the size of a witness for a key query. The sizes of several upward-closed sets that arise in the theory of Petri nets as well as in backward-reachability analysis in automated verification are derived in this paper, improving upon previous decidability results shown in the literature.