{"paper":{"title":"Generalized Homogeneous Polynomials for Efficient Template-Based Nonlinear Invariant Synthesis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LO","cs.SC","cs.SE"],"primary_cat":"cs.PL","authors_text":"Kensuke Kojima, Kohei Suenaga, Minoru Kinoshita","submitted_at":"2016-04-25T11:07:05Z","abstract_excerpt":"The template-based method is one of the most successful approaches to algebraic invariant synthesis. In this method, an algorithm designates a template polynomial p over program variables, generates constraints for p=0 to be an invariant, and solves the generated constraints. However, this approach often suffers from an increasing template size if the degree of a template polynomial is too high.\n  We propose a technique to make template-based methods more efficient. Our technique is based on the following finding: If an algebraic invariant exists, then there is a specific algebraic invariant t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.07201","kind":"arxiv","version":3},"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"}