The commutation of finite sets: a challenging problem
Theoretical Computer Science
Factorizations of languages and commutativity conditions
Acta Cybernetica
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]
On the Centralizer of a Finite Set
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
The Commutation with Codes and Ternary Sets of Words
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
The branching point approach to Conway's problem
Formal and natural computing
Fundamenta Informaticae
Outfix-Free Regular Languages and Prime Outfix-Free Decomposition
Fundamenta Informaticae
Prime decompositions of regular prefix codes
CIAA'02 Proceedings of the 7th international conference on Implementation and application of automata
A local search algorithm for grammatical inference
ICGI'10 Proceedings of the 10th international colloquium conference on Grammatical inference: theoretical results and applications
Overlap-Free regular languages
COCOON'06 Proceedings of the 12th annual international conference on Computing and Combinatorics
Prime decomposition problem for several kinds of regular codes
ICTAC'06 Proceedings of the Third international conference on Theoretical Aspects of Computing
Outfix-free regular languages and prime outfix-free decomposition
ICTAC'05 Proceedings of the Second international conference on Theoretical Aspects of Computing
Fundamenta Informaticae
Outfix-Free Regular Languages and Prime Outfix-Free Decomposition
Fundamenta Informaticae
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Representations of finite languages as a product (catenation) of languages are investigated, where the factor languages are "prime", that is, cannot be decomposed further in a nontrivial manner. In general, such prime decompositions are not unique - even the number of factors can vary exponentially. The paper investigates the uniqueness of prime decompositions, as well as the commuting of the factors. Interconnections to languages more general than finite are pointed out. In the case of regular languages, the notion of a decomposition set turns out to be a powerful tool.