{"paper":{"title":"Efficient tests for equivalence of hidden Markov processes and quantum random walks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Alexander Sch\\\"onhuth, Ulrich Faigle","submitted_at":"2008-08-20T22:53:12Z","abstract_excerpt":"While two hidden Markov process (HMP) resp. quantum random walk (QRW) parametrizations can differ from one another, the stochastic processes arising from them can be equivalent. Here a polynomial-time algorithm is presented which can determine equivalence of two HMP parametrizations $\\cM_1,\\cM_2$ resp. two QRW parametrizations $\\cQ_1,\\cQ_2$ in time $O(|\\S|\\max(N_1,N_2)^{4})$, where $N_1,N_2$ are the number of hidden states in $\\cM_1,\\cM_2$ resp. the dimension of the state spaces associated with $\\cQ_1,\\cQ_2$, and $\\S$ is the set of output symbols. Previously available algorithms for testing eq"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0808.2833","kind":"arxiv","version":5},"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"}