Satoshi Taoka

An improved heuristic algorithm FEIDEQ for the maximum legal firing sequence problem of Petri nets

The paper proposes a heuristic algorithm FEIDEQ for the maximum legal firing sequence problem of Petri nets (MAX LFS for short) and evaluates it based on experimental results. FEIDEQ is improved from FSDC that has been known to have the highest capability among the existing ones, by incorporating a new selection rule of transitions. In our experimental evaluation, FEIDEQ is applied to 2540 test problems, and, for each of 2040 of them, existence of an optimum solution is guaranteed. Among these 2040 test problems, FEIDEQ has produced an optimum solution to each of 1864 (91.3%) test problems, showing about 2.57 times that of FSDC, the best one so far. Furthermore, by adopting improved backtracking, average CPU time is about 0.86 times that of FSDC for general nets

Siphon-Trap-Based Algorithms for Efficiently Computing Petri Net Invariants

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 t 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 Yt · A = Ō 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 given 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, more minimal-support nonnegative integer invariants than any existing algorithm.