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Consider the problem of Linearly Constrained Convex Quadratic Programming. Under reasonable assumptions (the problem is feasible, the system of constraints is regular at every point, and the quadratic objective is strongly convex), the active-set method terminates after finitely many steps, and yields a global solution to the problem.
An example of a problem where this method has been used is the clique problem: given a CNF formula consisting of c clauses, the corresponding graph consists of a vertex for each literal, and an edge between each two non-contradicting [c] literals from different clauses; see the picture.
The left figure below shows a binary decision tree (the reduction rules are not applied), and a truth table, each representing the function (,,).In the tree on the left, the value of the function can be determined for a given variable assignment by following a path down the graph to a terminal.
An important set of problems in computational complexity involves finding assignments to the variables of a Boolean formula expressed in conjunctive normal form, such that the formula is true. The k -SAT problem is the problem of finding a satisfying assignment to a Boolean formula expressed in CNF in which each disjunction contains at most k ...
The concept of a stable model, or answer set, is used to define a declarative semantics for logic programs with negation as failure.This is one of several standard approaches to the meaning of negation in logic programming, along with program completion and the well-founded semantics.
The subset sum problem (SSP) is a decision problem in computer science. In its most general formulation, there is a multiset S {\displaystyle S} of integers and a target-sum T {\displaystyle T} , and the question is to decide whether any subset of the integers sum to precisely T {\displaystyle T} . [ 1 ]
In set theory, is also used to indicate 'not in the set of': is the set of all members of U that are not members of A. Regardless how it is notated or symbolized , the negation ¬ P {\displaystyle \neg P} can be read as "it is not the case that P ", "not that P ", or usually more simply as "not P ".
Resolution, a method for combining pairs of constraints to make additional valid constraints, also leads to a polynomial time solution. The 2-satisfiability problems provide one of two major subclasses of the conjunctive normal form formulas that can be solved in polynomial time; the other of the two subclasses is Horn-satisfiability.