{"paper":{"title":"Reachability in Higher-Order-Counters","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.FL","authors_text":"Alexander Heu{\\ss}ner, Alexander Kartzow","submitted_at":"2013-06-05T11:54:53Z","abstract_excerpt":"Higher-order counter automata (\\HOCS) can be either seen as a restriction of higher-order pushdown automata (\\HOPS) to a unary stack alphabet, or as an extension of counter automata to higher levels. We distinguish two principal kinds of \\HOCS: those that can test whether the topmost counter value is zero and those which cannot.\n  We show that control-state reachability for level $k$ \\HOCS with $0$-test is complete for \\mbox{$(k-2)$}-fold exponential space; leaving out the $0$-test leads to completeness for \\mbox{$(k-2)$}-fold exponential time. Restricting \\HOCS (without $0$-test) to level $2$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.1069","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"}