Formal languages
Handbook of Formal Languages
Theory of Automata
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
Obtaining shorter regular expressions from finite-state automata
Theoretical Computer Science
Fundamenta Informaticae
On the existence of prime decompositions
Theoretical Computer Science
Outfix-Free Regular Languages and Prime Outfix-Free Decomposition
Fundamenta Informaticae
Language Decompositions, Primality, and Trajectory-Based Operations
CIAA '08 Proceedings of the 13th international conference on Implementation and Applications of Automata
Length Codes, Products of Languages and Primality
Language and Automata Theory and Applications
Conjugacy of finite biprefix codes
Theoretical Computer Science
Variants of codes and indecomposable languages
Information and Computation
On language decompositions and primality
Rainbow of computer science
Language equations with complementation: Expressive power
Theoretical Computer Science
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
The generalization of generalized automata: expression automata
CIAA'04 Proceedings of the 9th international conference on Implementation and Application of Automata
Semantic shuffle on and deletion along trajectories
DLT'04 Proceedings of the 8th international conference on Developments in Language Theory
Outfix-free regular languages and prime outfix-free decomposition
ICTAC'05 Proceedings of the Second international conference on Theoretical Aspects of Computing
Prime decompositions of regular languages
DLT'06 Proceedings of the 10th international conference on Developments in Language Theory
Fundamenta Informaticae
Outfix-Free Regular Languages and Prime Outfix-Free Decomposition
Fundamenta Informaticae
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Representations of 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 do not necessarily exist. If they exist, they are not necessarily unique - the number of factors can vary even exponentially. The paper investigates prime decompositions, as well as the commuting of the factors, especially for the case of finite languages. In particular, a technique about commuting is developed in Section 4, where the factorization of languages L1 and L2 is discussed under the assumption L1L2 = L2L1.