An O(n1.5) algorithm to decide boundedness for conflict-free vector replacement systems
Information Processing Letters
Problems concerning fairness and temporal logic for conflict-free Petri nets
Theoretical Computer Science
Dynamic maintenance of directed hypergraphs
Theoretical Computer Science - Special issue on the Thirteenth Colleque sur les Arbres en Alge`bre et en Programmation Nancy, March 1988
A Unified High-Level Petri Net Formalism for Time-Critical Systems
IEEE Transactions on Software Engineering
A taxonomy of fairness and temporal logic problems for Petri nets
Theoretical Computer Science
On-line algorithms for polynomially solvable satisfiability problems
Journal of Logic Programming
A polynomial-time algorithm to decide liveness of bounded free choice nets
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A unified approach for deciding the existence of certain Petri net paths
Information and Computation
Complexity results for 1-safe nets
Theoretical Computer Science
Efficiency of a Good But Not Linear Set Union Algorithm
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Properties of Conflict-Free and Persistent Petri Nets
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Graph Algorithms for Functional Dependency Manipulation
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ACM Computing Surveys (CSUR)
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Introduction to Algorithms
A Fundamental Tehoerem of Asynchronous Parallel Computation
Proceedings of the Sagamore Computer Conference on Parallel Processing
A fully dynamic reachability algorithm for directed graphs with an almost linear update time
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Graphs and Hypergraphs
A Note on Persistent Petri Nets
Concurrency, Graphs and Models
SWAT '74 Proceedings of the 15th Annual Symposium on Switching and Automata Theory (swat 1974)
Linear connectivity problems in directed hypergraphs
Theoretical Computer Science
Combined siphon and marking generation for deadlock prevention in Petri nets
IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans
Journal of Computer and System Sciences
Journal of Computer and System Sciences
Analysis of modularly composed nets by siphons
IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans
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We introduce the notion of a T-path within Petri nets, and propose to adopt the model of directed hypergraphs in order to determine properties of nets; in particular, we study the relationships between T-paths and firable sequences of transitions. Let us consider a Petri net P= and the set of places with a positive marking in M"0, i.e., P"0={p|M"0(p)0}. If we regard the net as a directed graph, the existence of a simple path from any place in P"0 to a transition t is, of course, a necessary condition for the potential firability of t. This is sufficient only if the net is a state machine, where |^*t|=|t^*|=1 for all t@?T. In this paper we show that the existence of a T-path from any subset of P"0 to a transition t is a more restrictive condition and is, again, a necessary condition for the potential firability of t. But, in this case: (a) if P is a conflict-free Petri net, this is also a sufficient condition, (b) if P is a general Petri net, t is potentially firable by increasing the number of tokens inP"0. For conflict-free nets (CFPN) we consider the following problems: (a) determining the set of firable transitions, (b) determining the set of coverable places, (c) determining the set of live transitions, (d) deciding the boundedness of the net. For all these problems we provide algorithms requiring linear space and time, i.e., O(|P|+|T|+|A|), for a net P=. Previous results for this class of networks are given by Howell et al. (1987) [20], providing algorithms for solving problems in conflict-free nets in O(|P|x|T|) time and space. Given a Petri net and a marking M, the well-known coverability problem consists in finding a reachable marking M^' such that M^'=M; this problem is known to be EXPSPACE hard (Rackoff (1978)[33]). For general Petri nets we provide a partial answer to this problem. M is coverable by augmentation if it is coverable from an augmented markingM"0^' of the initial marking M"0: M"0^'=M"0 and, for all p@?P, M"0^'(p)=0 if M"0(p)=0. We solve this problem in linear time. The algorithms for computing T-paths are incremental: it is possible to modify the network (adding new places, transitions, arcs, tokens), and update the set of potentially firable transitions and coverable places without recomputing them from scratch. This feature is meaningful when used during the interactive design of a system.