Abstract
Construction problem of Petri net is dealt with. The problem is defined as following: Construct the Petri net with minimal number of transitions from which execution specified given marking sequences results, supposed that one or more transitions enabled at discrete time k=0, 1, … are allowed to fire simultaneously.
The problem mentioned above can be changed into following Construction Problem, taking into account integer vector which represents connection of a transition with all places for each transition: [Construction Problem] Let D be set of integer vectors which represent changes between markings of given marking sequences. Find a minimal set S0F of integer vectors satisfies following conditions for D: (1) any element of D can be represented as linear combination of elements of S0F and all of whose coefficients are 0 or 1, (2) considering transitions represented their connection with places by the elements of S0F, each transition is always enabled when its firing is required.
One of methods to obtain solutions of the Construction Problem is given. The method given in this paper is as following: Find the minimal cardinality |S0| of sets of integer vectors satisfy the condition (1) for D, and check for q whether there is a set of integer vectors with cardinality q which satisfy the condition (1) and (2) for D, increasing q from |S0| by one at time.
