The power of commuting with finite sets of words

Authors:
Michal Kunc
Affiliations:
Department of Mathematics, Masaryk University, Brno, Czech Republic
Venue:
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
Year:
2005

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Abstract

We show that one can construct a finite language L such that the largest language commuting with L is not recursively enumerable. This gives a negative answer to the question raised by Conway in 1971 and also strongly disproves Conway's conjecture on context-freeness of maximal solutions of systems of semi-linear inequalities.