Abstract
It is established that the subset of freek-generated subsemigroups of the semigroup of all automaton transformations over a finite alphabet is a second category set (in the sense of the Baire category approach) in the set of allk-generated subsemigroups. A continuum series of pairs of automaton transformations each of which generates a free semigroup of rank two is indicated. A criterion is established for this semigroup to be a finite-automaton group.
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Translated fromMatematicheskie Zametki, Vol. 63, No. 2, pp. 248–259, February, 1998.
The author wishes to express his deep gratitude to Professor V. I. Sushchans'kii for permanent help and attention to the research.
This research was partially supported by the ISSEP under grant No. GSU 051341.
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Oliinyk, A.S. On free semigroups of automaton transformations. Math Notes 63, 215–224 (1998). https://doi.org/10.1007/BF02308761
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DOI: https://doi.org/10.1007/BF02308761