Analysis of conservational transition systems
Y. Edmund Lien · 1973
Let V = {A1,A2,..An} be a finite set of symbols. V* denotes the free monoid generated by V with the cummutative operator “+”; that is, an element in V* can be written as [equation] where ai are nonnegative integers. Let x= [equation] and y = [equation]. We say x ≤ y if ai ≤ bi for l ≤ i ≤ n. An element in V* × V*, represented by x → y, is called a transition. Given a finite set T of transitions and S = [equation] some transition [equation] → [equation] can be fired if [equation] ≤ S. Firing of this transition results in a new element [equation](si - ai + bi)Ai. The triple is called a transition system. The notion of transition system was developed as a result of the study of Petri nets and vector addition systems.1 In this paper we study a special class of transition systems. A transition system is said to be conservational if there exists a function f:V &ran →{1,2,3...}, such that for every transition [equation] → [equation] it is true that [equation](Ai) = [equation]. Termination, repetitivity, and deadlock properties of conservational transition systems are studied.