A logical formalism for the study of the finite behaviour of Petri nets

Abstract

For languages recognized by finite automata we have two formalisms at our disposal: regular expressions (Kleene [3]) and logical formulas (Büchi [2]). In the case of Petri net languages there is no formalism like regular expressions. We give here a Büchi-like theorem which characterizes Petri net languages in terms of second order logical formulas.

This characterization situates exactly the power of Petri nets with respect to finite automata; roughly speaking, Petri nets are finite automata plus the ability of testing if a string of parentheses is well formed (in this paper "parentheses" always means the usual one sort of parentheses);

From a more practical point of view, the logical formalism has two advantages: 1. given a language, it enables us to easily prove that it is a Petri net language; 2. it gives an automatic procedure to construct a Petri net having a definite behaviour

The paper is organized as follows: in section 1 we present the Petri net formalism and the logical formalism. The proofs of the main results are sketched in section 2 (for details of them cf. [5]). Examples and applications are given in section 3.