Efficient Solution to Some Problems in Free Partially Commutative Monoids

In theoretical computer science, and, in particular, in automata and formal language theory, questions arise concerning words and sets of words in free monoids. Results and techniques from the study of the combinatorial algebra of the free monoid have provided an “algebraic” basis for dealing with many of these questions. In recent years there has been increasing interest in properties of words and sets of words in free partially commutative monoids or commutation monoids, that is, monoids in which some pairs of generating letters commute but no other relations hold. Some of this interest is due to the use of free partially commutative monoids in modeling problems of concurrency control in databases and parallel computation, as, for example, by Fle and Roucairol (1985); in a recent survey, Aalbersberg and Rozenberg (1988) have presented the connections between free partially commutative monoids and Petri nets. As in the case of free monoids, problems about words are linked to combinatorial properties, and the combinatorial algebra of free partially commutative monoids has