{"paper":{"title":"Some Languages Recognized by Two-Way Finite Automata with Quantum and Classical States","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Daowen Qiu, Lvzhou Li, Shenggen Zheng","submitted_at":"2011-12-13T10:14:41Z","abstract_excerpt":"{\\it Two-way finite automata with quantum and classical states} (2QCFA) were introduced by Ambainis and Watrous, and it was shown that 2QCFA have superiority over {\\it two-way probabilistic finite automata} (2PFA) for recognizing some non-regular languages such as the language $L_{eq}=\\{a^{n}b^{n}\\mid n\\in \\mathbf{N}\\}$ and the palindrome language $L_{pal}=\\{\\omega\\in \\{a,b\\}^*\\mid\\omega=\\omega^R\\}$, where $x^R$ is $x$ in the reverse order. It is interesting to find more languages like these that witness the superiority of 2QCFA over 2PFA. In this paper, we consider the language $L_{m}=\\{xcy\\m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.2844","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"}