{"paper":{"title":"Testing for Synchronization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.FL","authors_text":"Mikhail V. Berlinkov","submitted_at":"2014-01-11T18:04:38Z","abstract_excerpt":"We consider the first problem that appears in any application of synchronizing automata, namely, the problem of deciding whether or not a given $n$-state $k$-letter automaton is synchronizing. First we generalize results from \\cite{RandSynch},\\cite{On2Problems} for the case of strongly connected partial automata. Specifically, for $k>1$ we show that an automaton is synchronizing with probability $1-O(\\frac{1}{n^{0.5k}})$ and present an algorithm with linear in $n$ expected time, while the best known algorithm is quadratic on each instance. This results are interesting due to their applications"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.2553","kind":"arxiv","version":4},"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"}