Commutative grammars: the complexity of uniform word problems
Information and Control
Minimal solutions of linear diophantine systems: bounds and algorithms
RTA-91 Proceedings of the 4th international conference on Rewriting techniques and applications
On reachability equivalence for BPP-nets
Theoretical Computer Science
Properties of Conflict-Free and Persistent Petri Nets
Journal of the ACM (JACM)
The Complexity of Semilinear Sets
Proceedings of the 7th Colloquium on Automata, Languages and Programming
Distributed Bisimularity is Decidable for a Class of Infinite State-Space Systems
CONCUR '92 Proceedings of the Third International Conference on Concurrency Theory
Bisimulation Equivalence is Decidable for Basic Parallel Processes
CONCUR '93 Proceedings of the 4th International Conference on Concurrency Theory
Regularity is Decidable for Normed PA Processes in Polynomial Time
Proceedings of the 16th Conference on Foundations of Software Technology and Theoretical Computer Science
Tableau Methods for PA-Processes
TABLEAUX '97 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
On the Complexity of Bisimulation Problems for Basic Parallel Processes
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
An algorithm for the general Petri net reachability problem
STOC '81 Proceedings of the thirteenth annual ACM symposium on Theory of computing
Journal of Computer and System Sciences
Petri Nets, Commutative Context-Free Grammars, and Basic Parallel Processes
Fundamenta Informaticae
| Hi-index | 0.00 |
Yen proposed a construction for a semilinear representation of the reachability set of BPP-Petri nets which can be used to decide the equivalence problem of two BPP-PNs in doubly exponential time. We first address a gap in this construction which therefore does not always represent the reachability set. We propose a solution which is formulated in such a way that a large portion of Yen's construction and proof can be retained, preserving the size of the semilinear representation and the double exponential time bound (except for possibly larger values of some constants). In the second part of the paper, we propose very efficient algorithms for several variations of the boundedness and liveness problems of BPP-PNs. For several more complex notions of boundedness, as well as for the covering problem, we show NP-completeness. To demonstrate the contrast between BPP-PNs and a slight generalization regarding edge multiplicities, we show that the complexity of the classical boundedness problem increases from linear time to coNP-hardness. Our results also imply corresponding complexity bounds for related problems for process algebras and (commutative) context-free grammars.