{"paper":{"title":"On Recurrent Reachability for Continuous Linear Dynamical Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.SY","authors_text":"James Worrell, Joel Ouaknine, Ventsislav Chonev","submitted_at":"2015-07-13T21:56:48Z","abstract_excerpt":"The continuous evolution of a wide variety of systems, including continuous-time Markov chains and linear hybrid automata, can be described in terms of linear differential equations. In this paper we study the decision problem of whether the solution $\\boldsymbol{x}(t)$ of a system of linear differential equations $d\\boldsymbol{x}/dt=A\\boldsymbol{x}$ reaches a target halfspace infinitely often. This recurrent reachability problem can equivalently be formulated as the following Infinite Zeros Problem: does a real-valued function $f:\\mathbb{R}_{\\geq 0}\\rightarrow\\mathbb{R}$ satisfying a given li"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.03632","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"}