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A Horn formula is a propositional formula formed by conjunction of Horn clauses. Horn satisfiability is actually one of the "hardest" or "most expressive" problems which is known to be computable in polynomial time, in the sense that it is a P-complete problem. [1] The Horn satisfiability problem can also be asked for propositional many-valued ...
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.
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 ...
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.
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 ...
More generally, one can define a weighted version of MAX-SAT as follows: given a conjunctive normal form formula with non-negative weights assigned to each clause, find truth values for its variables that maximize the combined weight of the satisfied clauses. The MAX-SAT problem is an instance of Weighted MAX-SAT where all weights are 1. [5] [6 ...
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The dual concept to satisfiability is validity; a formula is valid if every assignment of values to its variables makes the formula true. For example, x + 3 = 3 + x {\displaystyle x+3=3+x} is valid over the integers, but x + 3 = y {\displaystyle x+3=y} is not.