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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 ...
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. [ 2 ]
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.
He constructs a PCP Verifier for 3-SAT that reads only 3 bits from the Proof. For every ε > 0, there is a PCP-verifier M for 3-SAT that reads a random string r of length ( ()) and computes query positions i r, j r, k r in the proof π and a bit b r. It accepts if and only if 'π(i r) ⊕ π(j r) ⊕ π(k r) = b r.
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 model theory, an atomic formula is satisfiable if there is a collection of elements of a structure that render the formula true. [4] If A is a structure, φ is a formula, and a is a collection of elements, taken from the structure, that satisfy φ, then it is commonly written that A ⊧ φ [a]
Example of a planar SAT problem. The black edges correspond to non-inverted variables and the red edges correspond to inverted variables. In computer science, the planar 3-satisfiability problem (abbreviated PLANAR 3SAT or PL3SAT) is an extension of the classical Boolean 3-satisfiability problem to a planar incidence graph.
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