{"paper":{"title":"Probabilistic Computers (So Quantum Computers) Are More Rigorously Powerful Than Traditional Computers, and Derandomization","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"cs.CC","authors_text":"Tianrong Lin","submitted_at":"2023-08-18T13:28:02Z","abstract_excerpt":"In this paper, we extend the techniques used in our previous work to show that there exists a probabilistic Turing machine running within time $O(n^k)$ for all $k\\in\\mathbb{N}_1$ accepting a language $L_d$ that is different from any language in $\\mathcal{P}$, and then further to prove that $L_d\\in\\mathcal{BPP}$, thus separating the complexity class $\\mathcal{BPP}$ from the class $\\mathcal{P}$ (i.e., $\\mathcal{P}\\subsetneqq\\mathcal{BPP}$).\n  Since the complexity class $\\mathcal{BQP}$ of {\\em bounded error quantum polynomial-time} contains the complexity class $\\mathcal{BPP}$ (i.e., $\\mathcal{BP"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.09549","kind":"arxiv","version":7},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2308.09549/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}