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The objective is the maximize or minimize the total sum of the weights of the satisfied clauses given a Boolean expression. weighted Max-SAT is the maximization version of this problem, and Max-SAT is an instance of weighted MAX-SAT problem where the weights of each clause are the same. The partial Max-SAT problem is the problem where some ...
3-satisfiability can be generalized to k-satisfiability (k-SAT, also k-CNF-SAT), when formulas in CNF are considered with each clause containing up to k literals. [ citation needed ] However, since for any k ≥ 3, this problem can neither be easier than 3-SAT nor harder than SAT, and the latter two are NP-complete, so must be k-SAT.
In computer science and mathematical logic, satisfiability modulo theories (SMT) is the problem of determining whether a mathematical formula is satisfiable.It generalizes the Boolean satisfiability problem (SAT) to more complex formulas involving real numbers, integers, and/or various data structures such as lists, arrays, bit vectors, and strings.
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
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It generalises the Boolean satisfiability problem (SAT) which is a decision problem considered in complexity theory. It is defined as: It is defined as: Given a 3-CNF formula Φ (i.e. with at most 3 variables per clause), find an assignment that satisfies the largest number of clauses.
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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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