Petri Nets Without Tokens

Abstract

For more than 40 years Petri nets [1] serve as an efficient formal model of concurrent behavior of complex discrete systems. There exists a rich bibliography of books and works devoted to these methods and many applications of nets have been already created. The model is extremely simple: it uses three basic concepts, of places, of transitions, and of a flow relation. The behavior of a net is represented by changing distribution of tokens situated in the net places, according to some simple rules (so-called firing rules). Non-negative integers play essential role in the description of tokens distribution, indicating the number of tokens contained in nets places and . Transitions determine way of changing the distribution, taking off a number of tokens from entry places and putting a number of tokens in exit places of an active transition. Formally, to any transition some operations on numbers stored in places are assigned and therefore the behavior of nets is described by means of a simple arithmetic with adding or subtracting operations on non-negative integers.