{"paper":{"title":"Semialgebraic Invariant Synthesis for the Kannan-Lipton Orbit Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LO","cs.SC","math.AG","math.NT"],"primary_cat":"cs.CC","authors_text":"Amaury Pouly, James Worrell, Jo\\\"el Ouaknine, Nathana\\\"el Fijalkow, Pierre Ohlmann","submitted_at":"2017-01-09T13:00:53Z","abstract_excerpt":"The \\emph{Orbit Problem} consists of determining, given a linear transformation $A$ on $\\mathbb{Q}^d$, together with vectors $x$ and $y$, whether the orbit of $x$ under repeated applications of $A$ can ever reach $y$. This problem was famously shown to be decidable by Kannan and Lipton in the 1980s.\n  In this paper, we are concerned with the problem of synthesising suitable \\emph{invariants} $\\mathcal{P} \\subseteq \\mathbb{R}^d$, \\emph{i.e.}, sets that are stable under $A$ and contain $x$ and not $y$, thereby providing compact and versatile certificates of non-reachability. We show that whether"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.02162","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"}