{"paper":{"title":"State succinctness of two-way finite automata with quantum and classical states","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.FL"],"primary_cat":"quant-ph","authors_text":"Daowen Qiu, Jozef Gruska, Lvzhou Li, Paulo Mateus, Shenggen Zheng","submitted_at":"2012-02-13T07:42:40Z","abstract_excerpt":"{\\it Two-way quantum automata with quantum and classical states} (2QCFA) were introduced by Ambainis and Watrous in 2002. In this paper we study state succinctness of 2QCFA.\n  For any $m\\in {\\mathbb{Z}}^+$ and any $\\epsilon<1/2$, we show that: {enumerate} there is a promise problem $A^{eq}(m)$ which can be solved by a 2QCFA with one-sided error $\\epsilon$ in a polynomial expected running time with a constant number (that depends neither on $m$ nor on $\\varepsilon$) of quantum states and $\\mathbf{O}(\\log{\\frac{1}{\\epsilon})}$ classical states, whereas the sizes of the corresponding {\\it determi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.2651","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"}