Orbits of linear maps and regular languages
Formal Languages and Automata Theory
2010-12-07 v2 Number Theory
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.
Keywords
Cite
@article{arxiv.1011.1842,
title = {Orbits of linear maps and regular languages},
author = {S. Tarasov and M. Vyalyi},
journal= {arXiv preprint arXiv:1011.1842},
year = {2010}
}
Comments
The text combines a journal publication and new results submitted to CSR 2011. 33 pages, 7 figures