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 (P B -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 P B -realizability problem with respect to computability we present some decidable and undecidable problems closely related to it. This paper is an extended version of the journal publication [16] and contains some additional results.
In REF , the Polyhedron Hitting Problem is related to decision problems in formal language theory.
Orbits of linear maps and regular languages
Vyalyi M., Tarasov S. Orbits of linear maps and regular languages. Discrete analysis and operations research. 2010. Vol. 17, No 6. P. 20--49 (in Russian)
Mathematics Computer Science