{"paper":{"title":"Range Avoidance in Boolean Circuits via Turan-type Bounds","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Jayalal Sarma, Neha Kuntewar","submitted_at":"2025-03-21T12:58:38Z","abstract_excerpt":"Given a circuit $C : \\{0,1\\}^n \\to \\{0,1\\}^m$ from a circuit class $F$, with $m > n$, finding a $y \\in \\{0,1\\}^m$ such that $\\forall x \\in \\{0,1\\}^n$, $C(x) \\ne y$, is the range avoidance problem (denoted by $F$-$avoid$). Deterministic polynomial time algorithms (even with access to $NP$ oracles) solving this problem is known to imply explicit constructions of various pseudorandom objects like hard Boolean functions, linear codes, PRGs etc. Deterministic polynomial time algorithms are known for $NC^0_2$-$avoid$ when $m > n$, and for $NC^0_3$-$avoid$ when $m \\ge \\frac{n^2}{\\log n}$, where $NC^0"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.17114","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/2503.17114/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"}