{"paper":{"title":"The Semialgebraic Orbit Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"James Worrell, Jo\\\"el Oukanine, Shaull Almagor","submitted_at":"2019-01-30T16:03:59Z","abstract_excerpt":"The Semialgebraic Orbit Problem is a fundamental reachability question that arises in the analysis of discrete-time linear dynamical systems such as automata, Markov chains, recurrence sequences, and linear while loops. An instance of the problem comprises a dimension $d\\in\\mathbb{N}$, a square matrix $A\\in\\mathbb{Q}^{d\\times d}$, and semialgebraic source and target sets $S,T\\subseteq \\mathbb{R}^d$. The question is whether there exists $x\\in S$ and $n\\in\\mathbb{N}$ such that $A^nx \\in T$. The main result of this paper is that the Semialgebraic Orbit Problem is decidable for dimension $d\\leq 3$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.11023","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"}