{"paper":{"title":"Separability of Reachability Sets of Vector Addition Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.FL","authors_text":"Charles Paperman, Lorenzo Clemente, S{\\l}awomir Lasota, Wojciech Czerwi\\'nski","submitted_at":"2016-09-01T12:42:18Z","abstract_excerpt":"Given two families of sets $\\mathcal{F}$ and $\\mathcal{G}$, the $\\mathcal{F}$ separability problem for $\\mathcal{G}$ asks whether for two given sets $U, V \\in \\mathcal{G}$ there exists a set $S \\in \\mathcal{F}$, such that $U$ is included in $S$ and $V$ is disjoint with $S$. We consider two families of sets $\\mathcal{F}$: modular sets $S \\subseteq \\mathbb{N}^d$, defined as unions of equivalence classes modulo some natural number $n \\in \\mathbb{N}$, and unary sets. Our main result is decidability of modular and unary separability for the class $\\mathcal{G}$ of reachability sets of Vector Additio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.00214","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"}