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## Canonical decomposition of a catenation of factorial languages

Venue: | Siberian Electronic Mathematical Reports 4 (2007) 14–22 |

Citations: | 1 - 1 self |

### Citations

19 | The power of commuting with finite sets of words”,
- Kunc
- 2007
(Show Context)
Citation Context ...nation. Even easiest questions tend to have very complicated answers. In particular, the maximal solution X of the commutation equation LX = XL may be arbitrarily complicated: as it was shown by Kunc =-=[6]-=-, even if the language L is finite, the maximal language X commuting with it may be not recursively enumerable. This situation contrasts with that for words, since xy = yx for some words x and y impli... |

12 | A unique decomposition theorem for factorial languages.
- Avgustinovich, Frid
- 2005
(Show Context)
Citation Context ... decomposition of a catenation of two factorial languages whose canonical decompositions are given. 1. Introduction This paper continues a research of decompositions of factorial languages started in =-=[1, 2]-=- and inspired by the field of language equations and algebraic operations on languages in general (see, e. g., [7, 8] and references therein). As the development of the theory shows, even language exp... |

12 |
Decision problems for language equations with Boolean operations
- Okhotin
(Show Context)
Citation Context ...his paper continues a research of decompositions of factorial languages started in [1, 2] and inspired by the field of language equations and algebraic operations on languages in general (see, e. g., =-=[7, 8]-=- and references therein). As the development of the theory shows, even language expressions where the only used operation is catenation prove very difficult to work with. It seems that nothing resembl... |

4 | Commutation with codes, Theoret - Karhumäki, Latteux, et al. - 2005 |

3 | Canonical decomposition of a regular factorial language - Avgustinovich, Frid - 2006 |

3 | Simple Language Equations
- Kunc
(Show Context)
Citation Context ...his paper continues a research of decompositions of factorial languages started in [1, 2] and inspired by the field of language equations and algebraic operations on languages in general (see, e. g., =-=[7, 8]-=- and references therein). As the development of the theory shows, even language expressions where the only used operation is catenation prove very difficult to work with. It seems that nothing resembl... |

2 |
2002) Unavoidable patterns. In: M. Lothaire, Algebraic Combinatorics on Words, Cambridge University Press, to appear. Supported in part by RFBR grants 00-01-00916 and 02-01-00939
- Cassaigne
- 2002
(Show Context)
Citation Context ...selves to factorial languages. This family is large and widely investigated since it includes, e. g., languages of factors of finite or infinite words and languages avoiding patterns (in the sense of =-=[3]-=-). We can also consider the factorial closure of an arbitrary language. Furthermore, the class of factorial languages is closed under taking catenation, unit, and intersection, and constitutes a monoi... |

2 |
Algebraic combinatorics on words
- Diekert, Algorithm, et al.
- 2002
(Show Context)
Citation Context ...hows, even language expressions where the only used operation is catenation prove very difficult to work with. It seems that nothing resembling the Makanin’s algorithm for word equations (see, e. g., =-=[4]-=-) can appear for language equations with catenation. Even easiest questions tend to have very complicated answers. In particular, the maximal solution X of the commutation equation LX = XL may be arbi... |

2 |
On the Decomposition of Finite Languages. Developments in Language Theory
- Salomaa, Yu
- 1997
(Show Context)
Citation Context ...z m for some word z and n, m ≥ 0. In some sense, the problems of catenation of languages are due to the fact that a unique factorization theorem is not valid for it: as it was shown by Salomaa and Yu =-=[9]-=-, even a finite unary language can admit several essentially different Frid, A. E., Catenation of factorial languages. c○ 2007 Frid A. E. The work is supported by RFFI (grants 05-01-00364 and 06-01-00... |