An algorithm for finding firing sequence based on generators for solutions of state equation in P/T Petri nets

We propose an algorithm for finding legal firing sequence for a nonnegative integer solution x/spl epsi/Z/sub +//sup n/spl times/1/ of state equation Ax=b of Petri nets. This algorithm first decides a finite number of generators which compose a solution x/spl epsi/Z/sub +//sup n/spl times/1/ out of the infinite set of solutions; X={x/spl epsi/Z/sub +//sup n/spl times/1/|Ax=b,A/spl epsi/Z/sup m/spl times/n/,b/spl epsi/Z/sup m/spl times/1/}. Secondly, after determining the expansion coefficients, we carry out finding firing sequence for a solution x by obtaining firing sequences of all decided and specified generators. The problem is that the firing sequence cannot be obtained from an inexecutable generator in this algorithm. Therefore this problem is solved such that an inexecutable generator is changed executable by combining with some other generators. By this time, this algorithm is efficient because Borrow information is used to combine generators.