{"paper":{"title":"Three Applications to Rational Relations of the High Undecidability of the Infinite Post Correspondence Problem in a Regular omega-Language","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","math.LO"],"primary_cat":"cs.LO","authors_text":"Olivier Finkel (ELM)","submitted_at":"2011-07-29T07:15:04Z","abstract_excerpt":"It was noticed by Harel in [Har86] that \"one can define $\\Sigma_1^1$-complete versions of the well-known Post Correspondence Problem\". We first give a complete proof of this result, showing that the infinite Post Correspondence Problem in a regular $\\omega$-language is $\\Sigma_1^1$-complete, hence located beyond the arithmetical hierarchy and highly undecidable. We infer from this result that it is $\\Pi_1^1$-complete to determine whether two given infinitary rational relations are disjoint. Then we prove that there is an amazing gap between two decision problems about $\\omega$-rational functio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.5886","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"}