论文信息 - On syntactic groups

On syntactic groups

We prove that for any finite prefix code X with n elements, the non special subgroups in the syntactic monoid of X have degree at most n − 1. This implies in particular that the groups in the syntactic monoid of X are all cyclic when X is a prefix code with three elements.

Dominique Perrin | Giuseppina Rindone | D. Perrin | G. Rindone

[1] Umberto Eco,et al. Theory of Codes , 1976 .

[2] Jean-Pierre Duval,et al. Periodes et Repetitions des Mots du Monoide Libre , 1979, Theor. Comput. Sci..

[3] Subgroups of free groups : a contribution to the Hanna Neumann conjecture , 2000 .

[4] Giuseppina Rindone. Construction d'une Famille de Codes Associes a Certains Groupes Finis , 1987, Theor. Comput. Sci..

[5] Maurice Pouzet,et al. Une caracterisation des mots periodiques , 1979, Discret. Math..

[6] J. C. Spehner. Les presentations des sous-monoides de rang 3 d'un monoide libre , 1981 .

[7] Giuseppina Rindone. Sur Les Groupes Syntaxiques D'un Langage , 1985, RAIRO Theor. Informatics Appl..

[8] Antonio Restivo,et al. Completing Codes , 1989, RAIRO Theor. Informatics Appl..

[9] Denis Derencourt. A Three-Word Code Which is Not Prefix-Suffix Composed , 1996, Theor. Comput. Sci..

[10] Giuseppina Rindone. Construction of a family of codes associated with certain finite groups , 1987 .

[11] Wojciech Rytter,et al. Text Algorithms , 1994 .

[12] Al. A. Markov. On finitely generated subsemigroups of a free semigroup , 1971 .

[13] J. Allouche. Algebraic Combinatorics on Words , 2005 .

[14] Juhani Karhumäki. Combinatorial and Computational Problems on Finite Sets of Words , 2001, MCU.

[15] Tero Harju,et al. Combinatorics on Words , 2004 .