Deciding Existence of Trace Codings (Abstract of Ph.D. thesis)

In 1977 Mazurkiewicz [14] proposed free partially commutative monoids as a tool for describing behaviour of concurrent systems. In this approach one represents elementary actions with letters of a given alphabet; then an observation of a finite run of a system is just a word over the alphabet. Two words are regarded as describing the same behaviour whenever they can be obtained from each other by commuting adjacent occurrences of letters representing concurrent actions. The mathematical formalization for this concept is provided by considering finitely presented monoids with their defining relations expressing commutativity of some of their generators. Possible behaviours of a system then correspond to congruence classes modulo the defining relations, which are called traces. In this way causal order of actions is distinguished from the order arising from sequentiality of observations.