{"paper":{"title":"Simulating Polynomial-Time Nondeterministic Turing Machines via Nondeterministic Turing Machines","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Tianrong Lin","submitted_at":"2024-06-15T02:54:55Z","abstract_excerpt":"We prove in this paper that there is a language $L_s$ accepted by some nondeterministic Turing machine that runs within time $O(n^k)$ for any positive integer $k\\in\\mathbb{N}_1$ but not by any ${\\rm co}\\mathcal{NP}$ machines. Then we further show that $L_s$ is in $\\mathcal{NP}$, thus proving a groundbreaking result that $$\\mathcal{NP}\\neq{\\rm co}\\mathcal{NP}. $$\n  The main techniques used in this paper are simulation and the novel new techniques developed in the author's recent work. Our main result has profound implications, such as $\\mathcal{P}\\neq\\mathcal{NP}$, etc. Further, if there exists"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.10476","kind":"arxiv","version":25},"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/2406.10476/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"}