Handbook of formal languages, vol. 1
Automata, Languages, and Machines
Automata, Languages, and Machines
On the Decomposition of Finite Languages
On the Decomposition of Finite Languages
The Commutation of Finite Sets: a Challenging Problem
The Commutation of Finite Sets: a Challenging Problem
On Fatou Properties of Rational Languages
On Fatou Properties of Rational Languages
On the Centralizer of a Finite Set
On the Centralizer of a Finite Set
The Commutation with Codes and Ternary Sets of Words
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
A Simple Undecidable Problem: The Inclusion Problem for Finite Substitutions on ab*c
STACS '01 Proceedings of the 18th Annual Symposium on Theoretical Aspects of Computer Science
Combinatorial and Computational Problems on Finite Sets of Words
MCU '01 Proceedings of the Third International Conference on Machines, Computations, and Universality
On the Complexity of Decidable Cases of Commutation Problem for Languages
FCT '01 Proceedings of the 13th International Symposium on Fundamentals of Computation Theory
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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.