{"paper":{"title":"Tighter Undecidability Bounds for Matrix Mortality, Zero-in-the-Corner Problems, and More","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Francois Nicolas, Julien Cassaigne, Tero Harju, Vesa Halava","submitted_at":"2014-04-02T18:10:40Z","abstract_excerpt":"We study the decidability of three well-known problems related to integer matrix multiplication: Mortality (M), Zero in the Left-Upper Corner (Z), and Zero in the Right-Upper Corner (R).\n  Let d and k be positive integers. Define M(k, d x d) as the following special case of the Mortality problem: given a set X of d -by-d integer matrices such that the cardinality of X is not greater than k, decide whether the d-by-d zero matrix belongs to X^+, where X^+ denotes the closure of X under the usual matrix multiplication. In the same way, define the Z(k, d x d) problem as: given an instance X of M(k"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.0644","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"}