Abstract
We prove that semigroups generated by reversible two-state Mealy automata have remarkable growth properties: they are either finite or free. We give an effective procedure to decide finiteness or freeness of such semigroups when the generating automaton is also invertible.
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Notes
Timings obtained on an Intel Xeon computer with clock speed 2.13GHz; programs written in GAP [12].
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Acknowledgements
I would like to thank Jean Mairesse and Matthieu Picantin for numerous discussions around this topic.
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An extended abstract was presented at STACS’13 [19].
The author is partially supported by ANR Project MealyM ANR-JCJC-12-JS02-012-01.
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Klimann, I. Automaton Semigroups: The Two-state Case. Theory Comput Syst 58, 664–680 (2016). https://doi.org/10.1007/s00224-014-9594-0
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DOI: https://doi.org/10.1007/s00224-014-9594-0