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In computer science and formal methods, a SAT solver is a computer program which aims to solve the Boolean satisfiability problem.On input a formula over Boolean variables, such as "(x or y) and (x or not y)", a SAT solver outputs whether the formula is satisfiable, meaning that there are possible values of x and y which make the formula true, or unsatisfiable, meaning that there are no such ...
UNAMBIGUOUS-SAT is the name given to the satisfiability problem when the input is restricted to formulas having at most one satisfying assignment. The problem is also called USAT. [24] A solving algorithm for UNAMBIGUOUS-SAT is allowed to exhibit any behavior, including endless looping, on a formula having several satisfying assignments.
The variant where variables are required to be 0 or 1, called zero-one linear programming, and several other variants are also NP-complete [2] [3]: MP1 Some problems related to Job-shop scheduling; Knapsack problem, quadratic knapsack problem, and several variants [2] [3]: MP9 Some problems related to Multiprocessor scheduling
Partial Max-SAT can be solved by first considering all of the hard clauses and solving them as an instance of SAT. The total maximum (or minimum) weight of the soft clauses can be evaluated given the variable assignment necessary to satisfy the hard clauses and trying to optimize the free variables (the variables that the satisfaction of the ...
If the first of these two equations were equated to "=1" as usual, one could find a proof π by solving a system of linear equations (see MAX-3LIN-EQN) implying P = NP. If z ∈ L, a fraction ≥ (1 − ε) of clauses are satisfied. If z ∉ L, then for a (1/2 − ε) fraction of R, 1/4 clauses are contradicted.
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
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.
Aspvall, Plass & Tarjan (1979) found a simpler linear time procedure for solving 2-satisfiability instances, based on the notion of strongly connected components from graph theory. [4] Two vertices in a directed graph are said to be strongly connected to each other if there is a directed path from one to the other and vice versa.
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