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On regular trace languages. (English) Zbl 0634.68076
Let A be a finite alphabet and let r be a symmetrical relation on A. Let us consider the free partially commutative monoid M(A,r) generated by A with respect to r (i.e., the quotient of A * by the congruence relation generated by (ab,ba) for all (a,b) in r). It is proved that the free partially commutative monoids M(A,r) whose regular sets form a Boolean algebra or are all unambiguous are the free products of free commutative monoids.
Reviewer: A.Stolboushkin

68Q45 Formal languages and automata
20M35 Semigroups in automata theory, linguistics, etc.
68Q70 Algebraic theory of languages and automata
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