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Automates et commutations partielles. (Automata and partial commutations). (French) Zbl 0601.68055
We consider words over an alphabet equipped with a partial commutation rule. The main result of the paper gives a sufficient condition for a set of words closed under the commutation rule to be recognizable by a finite automaton. More precisely, if X is recognizable and if ab\(\sim ba\) implies that the letters a and b do not appear in the same word of X, then the closure of \(X^*\) under the commutation rule is recognizable.

MSC:
68Q45 Formal languages and automata
20M05 Free semigroups, generators and relations, word problems
20M35 Semigroups in automata theory, linguistics, etc.
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References:
[1] 1. P. CARTIER et D. FOATA, Problèmes combinatoires de commutation et réarrangements, Lecture Notes in Math., n^\circ 85, 1969, Springer Verlag. Zbl0186.30101 MR239978 · Zbl 0186.30101
[2] 2. S. EILENBERG, Automata, Languages and Machines, vol. A, 1974, Academic Press. Zbl0317.94045 MR530382 · Zbl 0317.94045
[3] 3. M. P. FLÉ et G. ROUCAIROL, On Serializability of Iterated Transaction, A.C.M. SIGACT-SIGOPS, 1982, p. 194-200.
[4] 4. M. LOTHAIRE, Combinatorics on Words, 1983, Addison Wesley. Zbl0514.20045 MR675953 · Zbl 0514.20045
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