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New algebra bridges Boolean logic forms, avoids exponential blowup

Researchers have introduced a new representation language called power term polynomial algebra, designed to bridge the gap between conjunctive normal form (CNF) and algebraic normal form (ANF) for Boolean logic. This framework aims to avoid the exponential blowup often encountered during direct conversion between CNF and ANF by encoding structured monomials and CNF clauses within the representation itself. The proposed system includes algebraic operations for Boolean polynomial addition and multiplication, along with rewrite rules that allow for direct manipulation of formulas without full expansion into ANF, suggesting new avenues for structure-aware conversion and hybrid reasoning methods. AI

RANK_REASON The cluster contains an academic paper detailing a new theoretical framework for Boolean logic. [lever_c_demoted from research: ic=1 ai=0.4]

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  1. arXiv cs.AI TIER_1 English(EN) · Emanuele Sansone, Armando Solar-Lezama ·

    Power Term Polynomial Algebra for Boolean Logic

    arXiv:2603.13854v2 Announce Type: replace-cross Abstract: We introduce power term polynomial algebra, a representation language for Boolean formulae designed to bridge conjunctive normal form (CNF) and algebraic normal form (ANF). The language is motivated by the tiling mismatch …