REPRESENTATION OF COMPUTATIONS IN CONCURRENT AUTOMATA BY DEPENDENCE ORDERS

An automaton with concurrency relations A is a labelled transition sys tem with a collection of binary relations indicating when two actions in a given state of the automaton can occur independently of each othe r. The concurrency relations induce a natural equivalence relation for finite computation sequences. We investigate two graph-theoretic repr esentations of the equivalence classes of computation sequences and ob tain that under suitable assumptions on A they are isomorphic. Further more, the graphs are shown to carry a monoid operation reflecting prec isely the composition of computations. This generalizes fundamental gr aph-theoretical representation results due to Mazurkiewicz in trace th eory.