Representation of Computations in Concurrent Automata by Dependence Orders

An automaton with concurrency relations A is a labeled transition system with a collection of binary relations indicating when two actions in a given state of the automaton can occur independently of each other. The concurrency relations induce a natural equivalence relation for nite computation sequences. We investigate two graph-theoretic representations of the equivalence classes of computation sequences and obtain that under suitable assumptions on A they are isomorphic. Furthermore , the graphs are shown to carry a monoid operation reeecting precisely the composition of computations. This generalizes fundamental graph-theoretical representation results due to Mazurkiewicz in trace theory.