Reachability judgment in P/T Petri nets by approximate algebraic approach

  • Authors:

  • Tadashi Matsumoto;Masahiro Osogami;Seiichiro Moro

  • Affiliations:

  • Department of Electrical, Electronics and Computer Engineering, Fukui University of Technology, Fukui, Japan;Department of Management Information Science, Fukui University of Technology, Fukui, Japan;University of Fukui, Department of Electrical and Electronics Engineering, Fukui, Japan

  • Venue:
  • ISPRA'10 Proceedings of the 9th WSEAS international conference on Signal processing, robotics and automation
  • Year:
  • 2010

Quantified Score

Hi-index 0.00

Visualization

Abstract

Reachability is one of the most important behavioural properties of Petri nets. In this paper, an approximate algebraic approach to reachability judgment is proposed, where X; i.e., the set of all nonnegative integer solutions for state equation with the fixed marking-difference is approximately reduced to X*(⊂ X); i.e., the finite subset of X. A nonnegative integer solution, i.e., a firing count vector, x ∈ X* s.t. x ∈ Z+(n×1) is expressed by all elementary T-invariants and a particular solution in this paper. Firing executability, i.e., feasibility, for x ∈ X* is exactly tested by taking each elementary T-invariant as a checking processing unit, where x ∈ X* gives us, in general, global information and both of T-invariants and particular solutions give us local one of a given P/T Petri net. Merits and problems to be solved for the proposed method are outlined.