{"paper":{"title":"Delta-Complete Decision Procedures for Satisfiability over the Reals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SC"],"primary_cat":"cs.LO","authors_text":"Edmund Clarke, Jeremy Avigad, Sicun Gao","submitted_at":"2012-04-16T15:09:39Z","abstract_excerpt":"We introduce the notion of \"\\delta-complete decision procedures\" for solving SMT problems over the real numbers, with the aim of handling a wide range of nonlinear functions including transcendental functions and solutions of Lipschitz-continuous ODEs. Given an SMT problem \\varphi and a positive rational number \\delta, a \\delta-complete decision procedure determines either that \\varphi is unsatisfiable, or that the \"\\delta-weakening\" of \\varphi is satisfiable. Here, the \\delta-weakening of \\varphi is a variant of \\varphi that allows \\delta-bounded numerical perturbations on \\varphi. We prove t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.3513","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"}