MAX-2SAT
Reflections and Pedagogical Practices within the Scope of the Theory of Computation Course
DOI:
https://doi.org/10.20873/uft.2675-3588.2026.v7n2.p1-12Keywords:
Max-2SAT, NP-Completude, Redução Polinomial, Teoria da Complexidade, Satisfatibilidade BooleanaAbstract
This paper presents a formal and pedagogical demonstration of the NP-completeness of the Maximum 2-Satisfiability (Max-2SAT) problem through polynomial reduction from the Clique problem. Max-2SAT, a maximization variant of the SAT problem where each clause contains at most two literals, asks whether there exists a Boolean assignment capable of satisfying at least k clauses of a formula in conjunctive normal form. Although the 2-SAT problem is solvable in polynomial time, its maximization version is NP-complete. The demonstration employs a construction with an auxiliary variable that maps graph structures into Boolean formulas, establishing a bijective correspondence between cliques and satisfying assignments. As pedagogical contributions, this work presents: (i) detailed formal proof of NP-membership and NP-hardness; (ii) explicit construction of the Clique <=p Max-2SAT reduction with illustrative figures; (iii) complete step-by-step annotated example; (iv) pseudocode for the polynomial verifier; and (v) discussions about common pitfalls and comprehension strategies. The material produced aims to facilitate the learning of polynomial reductions and strengthen understanding of the boundary between tractability and computational intractability.
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Copyright (c) 2026 Raphael Sales de Souza, Thiago Gonzaga dos Santos, Daniel Martins da Silva, Tanilson Dias dos Santos
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