Years and Authors of Summarized Original Work
2003; Szeider
Problem Definition
Much research has been devoted to finding classes of propositional formulas in conjunctive normal form (CNF) for which the recognition problem as well as the propositional satisfiability problem (SAT) can be decided in polynomial time. Some of these classes form infinite chains \( { C_1 \subset C_2 \subset \cdots } \) such that every CNF formula is contained in some C k for k sufficiently large. Such classes are typically of the form \( { C_k=\{ F\in \text{CNF} \colon \pi(F) \leq k \} } \), where π is a computable mapping that assigns to CNF formulas F a non-negative integer \( { \pi(F) } \); we call such a mapping a satisfiability parameter. Since SAT is an NP-complete problem (actually, the first problem shown to be NP-complete [1]), we must expect that, the larger k, the longer the worst-case running times of the polynomial-time algorithms that recognize and decide satisfiability of formulas in C...
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Recommended Reading
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Szeider, S. (2016). Parameterized SAT. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_283
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