Geodesic
Orbits of linear maps and regular languages properties
Diskretnyj analiz i issledovanie operacij, Tome 17 (2010) no. 6, pp. 20-49

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We establish equivalence of two recognition problems: hitting of a polyhedral set by an orbit of a linear map and nonemptiness of the intersection of a regular language and the language of binary words permutations (the permutation filter). Decidability is unknown for both problems. The hitting problem generalizes well-known Skolem and nonnegativity problems that are formulated in terms of linear recurrence sequences. Bibliogr. 14.
Keywords: linear recurrence sequence, linear map, regular language, algorithmic decidability.
Mots-clés : orbit 
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M. N. Vyalyi; S. P. Tarasov. Orbits of linear maps and regular languages properties. Diskretnyj analiz i issledovanie operacij, Tome 17 (2010) no. 6, pp. 20-49. http://geodesic.mathdoc.fr/item/DA_2010_17_6_a1/