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arXiv · 1011.1842

Orbits of linear maps and regular languages

S. Tarasov·M. Vyalyi
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Abstract

We settle the equivalence between the problem of hitting a polyhedral set by the orbit of a linear map and the intersection of a regular language and a language of permutations of binary words (the permutation filter realizability problem). The decidability of the both problems is presently unknown and the first one is a straightforward generalization of the famous Skolem problem and the nonnegativity problem in the theory of linear recurrent sequences. To show a `borderline' status of the permutation filter realizability problem with respect to computability we present some decidable and undecidable problems closely related to it.

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S. Tarasov, M. Vyalyi. 2010-11-08. Orbits of linear maps and regular languages. https://arxiv.org/abs/1011.1842

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