{"paper":{"title":"Constant Time with Minimal Preprocessing, a Robust and Extensive Complexity Class","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"cs.DS","authors_text":"\\'Etienne Grandjean, Louis Jachiet","submitted_at":"2025-09-12T12:28:23Z","abstract_excerpt":"In this paper, we study the class $\\mathtt{cstPP}$ of operations $\\mathtt{op}: \\mathbb{N}^k\\to\\mathbb{N}$, of any fixed arity $k\\ge 1$, satisfying the following property: for each fixed integer $d\\ge 1$, there exists an algorithm for a RAM machine which, for any input integer $N\\ge 2$, - pre-computes some tables in $O(N)$ time, - then reads $k$ operands $x_1,\\ldots,x_k<N^d$ and computes $\\mathtt{op}(x_1,\\dots,x_k)$ in constant time.\n  We show that the $\\mathtt{cstPP}$ class is robust and extensive and satisfies several closure properties. It is invariant depending on whether the set of primiti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.10188","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2509.10188/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}