{"paper":{"title":"Gap Theorems for the Delay of Circuits Simulating Finite Automata","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Connor Ahlbach, Jeremy Usatine, Nicholas Pippenger","submitted_at":"2013-08-13T20:09:06Z","abstract_excerpt":"We study the delay (also known as depth) of circuits that simulate finite automata, showing that only certain growth rates (as a function of the number $n$ of steps simulated) are possible. A classic result due to Ofman (rediscovered and popularized by Ladner and Fischer) says that delay $O(\\log n)$ is always sufficient. We show that if the automaton is \"generalized definite\", then delay O(1) is sufficient, but otherwise delay $\\Omega(\\log n)$ is necessary; there are no intermediate growth rates. We also consider \"physical\" (rather than \"logical\") delay, whereby we consider the lengths of wire"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.2970","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"}