Exact Algorithms for General CNF SAT

Years and Authors of Summarized Original Work

1998; Hirsch 2003; Schuler

Problem Definition

The satisfiability problem (SAT) for Boolean formulas in conjunctive normal form (CNF) is one of the first NP-complete problems [2, 13]. Since its NP-completeness currently leaves no hope for polynomial-time algorithms, the progress goes by decreasing the exponent. There are several versions of this parametrized problem that differ in the parameter used for the estimation of the running time.

Problem 1 (SAT). 

INPUT: :

Formula F in CNF containing n variables, m clauses, and l literals in total.

OUTPUT: :

“Yes” if F has a $\underline{satisfying\ assignment}$, i.e., a substitution of Boolean values for the variables that makes F true. “No” otherwise.

The bounds on the running time of SAT algorithms can be thus given in the form $\vert F\vert ^{O(1)} \cdot \alpha ^{n}$, $\vert F\vert ^{O(1)} \cdot \beta ^{m}$, or $\vert F\vert ^{O(1)} \cdot \gamma ^{l}$, where $\vert F\vert$is the length...