{"paper":{"title":"Decomposition by tree dimension in Horn clause verification","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Bishoksan Kafle (Roskilde University, Denmark, Denmark), IMDEA Software Institute, John P. Gallagher (Roskilde University, Pierre Ganty (IMDEA Software Institute, Spain)","submitted_at":"2015-12-12T02:02:27Z","abstract_excerpt":"In this paper we investigate the use of the concept of tree dimension in Horn clause analysis and verification. The dimension of a tree is a measure of its non-linearity - for example a list of any length has dimension zero while a complete binary tree has dimension equal to its height. We apply this concept to trees corresponding to Horn clause derivations. A given set of Horn clauses P can be transformed into a new set of clauses P=<k, whose derivation trees are the subset of P's derivation trees with dimension at most k. Similarly, a set of clauses P>k can be obtained from P whose derivatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.03862","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"}