{"paper":{"title":"Elementary Deduction Problem for Locally Stable Theories with Normal Forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.CR"],"primary_cat":"cs.LO","authors_text":"Daniele Nantes-Sobrinho (Universidade de Bras\\'ilia), Maribel Fern\\'andez (King's College London), Mauricio Ayala-Rinc\\'on (Universidade de Bras\\'ilia)","submitted_at":"2013-03-29T09:01:51Z","abstract_excerpt":"We present an algorithm to decide the intruder deduction problem (IDP) for a class of locally stable theories enriched with normal forms.  Our result relies on a new and efficient algorithm to solve a restricted case of higher-order associative-commutative matching, obtained by combining the Distinct Occurrences of AC- matching algorithm and a standard algorithm to solve systems of linear Diophantine equations. A translation between natural deduction and sequent calculus allows us to use the same approach to decide the \\emphelementary deduction problem for locally stable theories. As an applic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.7328","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"}