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Playing with Conway’s problem. (English) Zbl 1156.68030
Summary: The centralizer of a language is the maximal language commuting with it. The question, raised by Conway in [J. H. Conway, Regular algebra and finite machines. London: Chapman and Hall (1971; Zbl 0231.94041)], whether the centralizer of a rational language is always rational, recently received a lot of attention. In [M. Kunc, “The power of commuting with finite sets of words”, Lect. Notes Comput. Sci. 3404, 569–580 (2005; Zbl 1119.68108)], a strong negative answer to this problem was given by showing that even complete co-recursively enumerable centralizers exist for finite languages. Using a combinatorial game approach, we give here an incremental construction of rational languages embedding any recursive computation in their centralizers.
MSC:
68Q45 Formal languages and automata
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