{"paper":{"title":"Canonical Logic Programs are Succinctly Incomparable with Propositional Formulas","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.LO","authors_text":"Xishun Zhao, Yuping Shen","submitted_at":"2014-12-01T01:10:30Z","abstract_excerpt":"\\emph{Canonical (logic) programs} (CP) refer to normal logic programs augmented with connective $not\\ not$. In this paper we address the question of whether CP are \\emph{succinctly incomparable} with \\emph{propositional formulas} (PF). Our main result shows that the PARITY problem, which can be polynomially represented in PF but \\emph{only} has exponential representations in CP. In other words, PARITY \\emph{separates} PF from CP. Simply speaking, this means that exponential size blowup is generally inevitable when translating a set of formulas in PF into an equivalent program in CP (without in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.0320","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"}