Orbits of linear maps and regular languages properties

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.