Abstract
We prove two results on commutation of languages. First, we show that the maximal language commuting with a three element language, i.e. its centralizer, is rational, thus giving an affirmative answer to a special case of a problem proposed by Conway in 1971. Second, we characterize all languages commuting with a three element code. The characterization is similar to the one proved by Bergman for polynomials over noncommuting variables, cf. Bergman, 1969 and Lothaire, 2000: A language commutes with a three element code X if and only if it is a union of powers of X.
The authors acknowledge the support from the Academy of Finland under project 44087.
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Karhumäki, J., Petre, I. (2000). On the Centralizer of a Finite Set. In: Montanari, U., Rolim, J.D.P., Welzl, E. (eds) Automata, Languages and Programming. ICALP 2000. Lecture Notes in Computer Science, vol 1853. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45022-X_45
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DOI: https://doi.org/10.1007/3-540-45022-X_45
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