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English: Gadgets for an NP-completeness proof of graph 3-coloring, by reduction from 3-Satisfiability.The variable and clause gadgets are shown on the upper and lower left, respectively, and the right side of the figure shows the complete reduction for the instance (x ∨ y ∨ ~z) ∧ (~x ∨ ~y ∨ z) with three variables and two clauses.
The problem of Horn satisfiability is solvable in linear time. [4] The problem of deciding the truth of quantified Horn formulae can be also solved in polynomial time. [5] A polynomial-time algorithm for Horn satisfiability is recursive:
A variant of the 3-satisfiability problem is the one-in-three 3-SAT (also known variously as 1-in-3-SAT and exactly-1 3-SAT). Given a conjunctive normal form with three literals per clause, the problem is to determine whether there exists a truth assignment to the variables so that each clause has exactly one TRUE literal (and thus exactly two ...
In the international SAT competitions, implementations based around DPLL such as zChaff [2] and MiniSat [3] were in the first places of the competitions in 2004 and 2005. [ 4 ] Another application that often involves DPLL is automated theorem proving or satisfiability modulo theories (SMT), which is a SAT problem in which propositional ...
The soft satisfiability problem (soft-SAT), given a set of SAT problems, asks for the maximum number of those problems which can be satisfied by any assignment. [16] The minimum satisfiability problem. The MAX-SAT problem can be extended to the case where the variables of the constraint satisfaction problem belong to the set
Unlike 3SAT, some variants of NAE3SAT in which graphs representing the structure of variables and clauses are planar graphs can be solved in polynomial time.In particular this is true when there exists a planar graph with one vertex per variable, one vertex per clause, an edge for each variable–clause incidence, and a cycle of edges connecting all the variable vertices.
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