{"paper":{"title":"Primitive sets of nonnegative matrices and synchronizing automata","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"cs.FL","authors_text":"Bal\\'azs Gerencs\\'er, Rapha\\\"el M. Jungers, Vladimir V. Gusev","submitted_at":"2016-02-24T15:26:19Z","abstract_excerpt":"A set of nonnegative matrices $\\mathcal{M}=\\{M_1, M_2, \\ldots, M_k\\}$ is called primitive if there exist indices $i_1, i_2, \\ldots, i_m$ such that $M_{i_1} M_{i_2} \\ldots M_{i_m}$ is positive (i.e. has all its entries $>0$). The length of the shortest such product is called the exponent of $\\mathcal{M}$. The concept of primitive sets of matrices comes up in a number of problems within control theory, non-homogeneous Markov chains, automata theory etc. Recently, connections between synchronizing automata and primitive sets of matrices were established. In the present paper, we significantly str"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.07556","kind":"arxiv","version":1},"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"}