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
The Branching Point Approach to Conway's Problem
Formal and Natural Computing - Essays Dedicated to Grzegorz Rozenberg [on occasion of his 60th birthday, March 14, 2002]
Some Decision Results for Recognizable Sets in Arbitrary Monoids
Proceedings of the Fifth Colloquium on Automata, Languages and Programming
On the Centralizer of a Finite Set
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
FCT '01 Proceedings of the 13th International Symposium on Fundamentals of Computation Theory
On the Decomposition of Finite Languages
On the Decomposition of Finite Languages
On the complexity of decidable cases of the commutation problem of languages
Theoretical Computer Science
Finite sets of words and computing
MCU'04 Proceedings of the 4th international conference on Machines, Computations, and Universality
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We prove several results on the commutation of languages. First, we prove that the largest set commuting with a given code X, i.e., its centralizer e(X), is always 驴(X)*, where 驴(X) is the primitive root of X. Using this result, we characterize the commutation with codes similarly as for words, polynomials, and formal power series: a language commutes with X if and only if it is a union of powers of 驴(X). This solves a conjecture of Ratoandromanana, 1989, and also gives an affirmative answer to a special case of an intriguing problem raised by Conway in 1971. Second, we prove that for any nonperiodic ternary set of words F 驴 驴+, e(F) = F*, and moreover, a language commutes with F if and only if it is a union of powers of F, results previously known only for ternary codes. A boundary point is thus established, as these results do not hold for all languages with at least four words.