The commutation of finite sets: a challenging problem
Theoretical Computer Science
Conway's problem for three-word sets
Theoretical Computer Science
Computation: finite and infinite machines
Computation: finite and infinite machines
Theoretical Computer Science - The art of theory
The Power of Commuting with Finite Sets of Words
Theory of Computing Systems
The power of commuting with finite sets of words
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
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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, Chapman Hall, 1971], whether the centralizer of a rational language is always rational, recently received a lot of attention. In Kunc [M. Kunc, The power of commuting with finite sets of words, in: Proc. of STACS 2005, in: LNCS, vol. 3404, Springer, 2005, pp. 569-580], 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.