{"paper":{"title":"On the Approximability of Parameterized Minimum Monotone Satisfying Assignment","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Bingkai Lin, Venkatesan Guruswami, Xin Zheng, Xuandi Ren","submitted_at":"2026-07-07T23:07:33Z","abstract_excerpt":"The parameterized Minimum Monotone Satisfying Assignment ($k$-MMSA) problem asks whether a monotone Boolean circuit admits a satisfying assignment of Hamming weight at most $k$. The MMSA hierarchy is defined by allowing a bounded number of alternations between AND and OR gates in the circuit. While the polynomial-time approximability of the MMSA hierarchy has been studied extensively, much less is known in the parameterized setting. In particular, $k$-MMSA$_2$ is the well-known $k$-SetCover problem, whose parameterized inapproximability lies in the $\\text{polylog}(n)$ regime. In contrast, $k$-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.06852","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/2607.06852/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"}