{"paper":{"title":"Pseudorandom bits for non-commutative programs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Chin Ho Lee, Emanuele Viola","submitted_at":"2025-06-02T16:21:30Z","abstract_excerpt":"We obtain new explicit pseudorandom generators for several computational models involving groups. Our main results are as follows:\n  1. We consider read-once group-products over a finite group $G$, i.e., tests of the form $\\prod_{i=1}^n g_i^{x_i}$ where $g_i\\in G$, a special case of read-once permutation branching programs. We give generators with optimal seed length $c_G \\log(n/\\varepsilon)$ over any $p$-group. The proof uses the small-bias plus noise paradigm, but derandomizes the noise to avoid the recursion in previous work. Our generator works when the bits are read in any order. Previous"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.01832","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.01832/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"}