{"paper":{"title":"Z_2-Algebras in the Boolean Function Irreducible Decomposition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Federico Zertuche, Martha Takane","submitted_at":"2012-08-01T16:50:51Z","abstract_excerpt":"We develop further the consequences of the irreducible-Boolean classification established in Ref. [9]; which have the advantage of allowing strong statistical calculations in disordered Boolean function models, such as the \\textit{NK}-Kauffman networks. We construct a ring-isomorphism $ mathfrak{R}_K {i_1, ..., i_\\lambda} \\cong \\mathcal{P}^2 -[K] $ of the set of reducible $K$-Boolean functions that are reducible in the Boolean arguments with indexes ${i_1, ..., i_\\lambda}$; and the double power set $\\mathcal{P}^2 [K]$, of the first $K$ natural numbers. This allows us, among other things, to ca"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.0332","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"}