Abstract
Boolean satisfiability (SAT) solvers are used heavily in hardware and software verification tools for checking satisfiability of Boolean formulas. Most state-of-the-art SAT solvers are based on the DPLL algorithm and require the input formula to be in conjunctive normal form (CNF). We represent the vhpform of a given NNF formula in the form of two graphs called vpgraph and hpgraph. The input formula is translated into a 2-dimensional format called vertical-horizontal path form (vhpform). In this form disjuncts (operands of ∨) are arranged orizontally and conjuncts (operands of ∧) are arranged vertically.The formula is satisfiable if and only if there exists a vertical path through this arrangement that does not contain two opposite literals ( l and ¬l). The input formula is not required to be in CNF.
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References
Cook, S.A.: The complexity of theorem-proving procedures. In: STOC, pp. 151–158 (1971), 1.1
Moskewicz, M.W., Madigan, C.F., Zhao, Y., Zhang, L., Malik, S.: Chaff: Engineering an efficient SAT solver. In: Design Automation Conference (DAC 2001), pp. 530–535 (June 2001), 1.1, 1.2.1,1.2.4, 3.7, 3.8, 4.2, 4.4.1
Plaisted, D.A., Greenbaum, S.: A structure-preserving clauseform translation. J. Symb. Comput. 2(3) (1986), 1.1, 2.1, 3.8, 4.10.2
Tseitin, G.S.: On the complexity of derivation in propositional calculus. In: Studies in Constructive Mathematics and Mathematical Logic, pp. 115–125 (1968), 1.1, 2.1, 4.10.2
Järvisalo, M., Junttila, T., Niemelä, I.: Unrestricted vs restricted cut in a tableau method for boolean circuits. Annals of Mathematics and Artificial Intelligence 44(4), 373–399 (2005), 1.1
Eén, N., Biere, A.: Effective Preprocessing in SAT Through Variable and Clause Elimination. In: Bacchus, F., Walsh, T. (eds.) SAT 2005. LNCS, vol. 3569, pp. 61–75. Springer, Heidelberg (2005), 1.1, 2.1
Andrews, P.B.: Theorem Proving via General Matings. J. ACM 28(2), 193–214 (1981), 1.1.1, 2, 3
Andrews, P.B.: An Introduction to Mathematical Logic and Type Theory: to Truth through Proof, 2nd edn. Kluwer Academic Publishers, Dordrecht (2002), 1.1.1, 2, 2.2, 1, 2.2, 2.2
Davis, M., Putnam, H.: A computing procedure for quantification theory. J. ACM 7(3), 201–215 (1960), 1.1, 2, 4
Takamizawa, K., Nishizeki, T., Saito, N.: Linear-time computability of combinatorial problems on series-parallel graphs. J. ACM 29(3), 623–641 (1982), 2.3.2
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Xie, R., Hai, B. (2012). Graph Based Representations SAT Solving for Non-clausal Formulas. In: Jin, D., Lin, S. (eds) Advances in Electronic Commerce, Web Application and Communication. Advances in Intelligent and Soft Computing, vol 149. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28658-2_2
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DOI: https://doi.org/10.1007/978-3-642-28658-2_2
Publisher Name: Springer, Berlin, Heidelberg
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