Descriptional Complexity of Formal Systems

Abstract

This paper investigates the universality problem for Petri nets with inhibitor arcs. Four descriptional complexity parameters are considered: the number of places, transitions, inhibitor arcs, and the maximal degree of a transition. Each of these parameters is aimed to be minimized, a special attention being given to the number of places. Four constructions are presented having the following values of parameters (listed in the above order): (5, 877, 1022, 729), (5, 1024, 1316, 379), (4, 668, 778, 555), and (4, 780, 1002, 299). The decrease of the number of places with respect to previous work is primarily due to the consideration of non-deterministic computations in Petri nets. Using equivalencies between models our results can be translated to multiset rewriting with forbidding conditions, or to P systems with inhibitors.