The interface between P and NP in signed CNF formulas

We first define a new class of signed CNF formulas and prove that its satisfiability problem is NP-complete. We then study in detail the interface between P and NP in two many-valued satisfiability problems: Mono+pPartiallySigned-2SAT and Regular+pSigned-2SAT. We show that such problems smoothly interpolate between P and NP by mixing together a polynomial and an NP-complete problem, and identify phase transition behavior in each of these problems.

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