Algorithms for Computation of Petri Net Invariants based on Siphon-Traps

摘要

A siphon-trap(ST) of a Petri net N = (P, T, E, α, β) is defined as a set S of places such that, for any transition t, there is an edge from i to a place of S if and only if there is an edge from a place of S to t. A P-invariant is a |P|-dimensional vector Y with Y{sup}t·A=0{top}- for the place-transition incidence matrix A of N. The Fourier-Motzkin method is well-known for computing all such invariants. This method, however, has a critical deficiency such that, even if a give Perti net N has any invariant, it is likely that no invariants are output because of memory overflow in storing intermediary vectors as candidates for invariants. In this paper, we propose an algorithm STFM_N for computing minimal-support nonnegative integer invariants: it tries to decrease the number of such candidate vectors in order to overcome this deficiency, by restricting computation of invariants to siphon-traps. It is shown, through experimental results, that STFM_N has high possibility of finding, if any, at least one more minimal-support nonnegative integer invariant then any existing algorithms.