{"paper":{"title":"Geometric Series as Nontermination Arguments for Linear Lasso Programs","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Jan Leike, Matthias Heizmann","submitted_at":"2014-05-17T15:42:32Z","abstract_excerpt":"We present a new kind of nontermination argument for linear lasso programs, called geometric nontermination argument. A geometric nontermination argument is a finite representation of an infinite execution of the form $(\\vec{x} + \\sum_{i=0}^t \\lambda^i \\vec{y})_{t \\geq 0}$. The existence of this nontermination argument can be stated as a set of nonlinear algebraic constraints. We show that every linear loop program that has a bounded infinite execution also has a geometric nontermination argument. Furthermore, we discuss nonterminating programs that do not have a geometric nontermination argum"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.4413","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"}