{"paper":{"title":"Upper bounds for Newton's method on monotone polynomial systems, and P-time model checking of probabilistic one-counter automata","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"cs.LO","authors_text":"Alistair Stewart, Kousha Etessami, Mihalis Yannakakis","submitted_at":"2013-02-15T12:48:20Z","abstract_excerpt":"A central computational problem for analyzing and model checking various classes of infinite-state recursive probabilistic systems (including quasi-birth-death processes, multi-type branching processes, stochastic context-free grammars, probabilistic pushdown automata and recursive Markov chains) is the computation of {\\em termination probabilities}, and computing these probabilities in turn boils down to computing the {\\em least fixed point} (LFP) solution of a corresponding {\\em monotone polynomial system} (MPS) of equations, denoted x=P(x).\n  It was shown by Etessami & Yannakakis that a dec"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.3741","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"}