Handbook of formal languages, vol. 1
On Fatou properties of rational languages
Where mathematics, computer science, linguistics and biology meet
The commutation of finite sets: a challenging problem
Theoretical Computer Science
Theory of Codes
Conway's problem for three-word sets
Theoretical Computer Science
Some Decision Results for Recognizable Sets in Arbitrary Monoids
Proceedings of the Fifth Colloquium on Automata, Languages and Programming
The Equivalence Problem of Finite Substitutions on ab*c, with Applications
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
The branching point approach to Conway's problem
Formal and natural computing
The power of commuting with finite sets of words
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
Theoretical Computer Science
Conjugacy of finite biprefix codes
Theoretical Computer Science
Simple equations on binary factorial languages
Theoretical Computer Science
What do we know about language equations?
DLT'07 Proceedings of the 11th international conference on Developments in language theory
Commutation of binary factorial languages
DLT'07 Proceedings of the 11th international conference on Developments in language theory
On language inequalities XK ⊆ LX
DLT'05 Proceedings of the 9th international conference on Developments in Language Theory
Finite sets of words and computing
MCU'04 Proceedings of the 4th international conference on Machines, Computations, and Universality
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The centralizer of a set of words X is the largest set of words C(X)commuting with X: XC(X) = C(X)X. It has been a long standing open question due to [J.H. Conway, Regular Algebra and Finite Machines, Chapman & Hall, London (1971).], whether the centralizer of any rational set is rational. While the answer turned out to be negative in general, see [M. Kunc, Proc. of ICALP 2004, Lecture Notes in Computer Science, Vol. 3142, Springer, Berlin, 2004, pp. 870-881.], we prove here that the situation is different for codes: the centralizer of any rational code is rational and if the code is finite, then the centralizer is finitely generated. This result has been previously proved only for binary and ternary sets of words in a series of papers by the authors and for prefix codes in an ingenious paper by [B. Ratoandromanana, RAIRO Inform. Theor. 23(4) (1989) 425-444.]--many of the techniques we use in this paper follow her ideas. We also give in this paper an elementary proof for the prefix case.