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Unambiguous regular trace languages. (English) Zbl 0627.68060
Algebra, combinatorics and logic in computer science, Colloq. Györ/Hung. 1983, vol. 1, Colloq. Math. Soc. János Bolyai 42, 113-123 (1986).
[For the entire collection see Zbl 0593.00024.]
It is a known result that so called unambiguous regular languages [S. Eilenberg and M. Schützenberger, Rational sets in commutative monoids, J. Algebra 13, 173-191 (1969; Zbl 0206.027)] coincide with the whole class of regular languages both in the case of fully commutative and of non-commutative monoids. In this paper these two classes of languages are compared in the case of partially commutative monoids represented here by traces of [A. Mazurkiewicz, Concurrent program schemes and their interpretations, DAIMI PB-78, Aarhus Univ. Press (1977)]. The main result is that these two classes coincide if and only if the independence relation is transitive.
Reviewer: R.Janicki

68Q45 Formal languages and automata