{"paper":{"title":"Orbits of linear maps and regular languages","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"cs.FL","authors_text":"M. Vyalyi, S. Tarasov","submitted_at":"2010-11-08T16:35:06Z","abstract_excerpt":"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 unde"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.1842","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}