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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 De Morgan dual is the canonical conjunctive normal form , maxterm canonical form, or Product of Sums (PoS or POS) which is a conjunction (AND) of maxterms. These forms can be useful for the simplification of Boolean functions, which is of great importance in the optimization of Boolean formulas in general and digital circuits in particular.
Using the laws of Boolean algebra, every propositional logic formula can be transformed into an equivalent conjunctive normal form, which may, however, be exponentially longer. For example, transforming the formula (x 1 ∧y 1) ∨ (x 2 ∧y 2) ∨ ... ∨ (x n ∧y n) into conjunctive normal form yields (x 1 ∨ x 2 ∨ … ∨ x n) ∧
The conjunctive normal form of a monotone function expresses the function as a conjunction ("and") of clauses, each of which is a disjunction ("or") of some of the variables. A clause may appear in the conjunctive normal form if it is true whenever the overall function is true; in this case it is called an implicate , because the truth of the ...
A formula of the predicate calculus is in prenex [1] normal form (PNF) if it is written as a string of quantifiers and bound variables, called the prefix, followed by a quantifier-free part, called the matrix. [2]
Instances of the 2-satisfiability problem are typically expressed as Boolean formulas of a special type, called conjunctive normal form (2-CNF) or Krom formulas. Alternatively, they may be expressed as a special type of directed graph , the implication graph , which expresses the variables of an instance and their negations as vertices in a ...
The Tseytin transformation, alternatively written Tseitin transformation, takes as input an arbitrary combinatorial logic circuit and produces an equisatisfiable boolean formula in conjunctive normal form (CNF). The length of the formula is linear in the size of the circuit. Input vectors that make the circuit output "true" are in 1-to-1 ...
In logic and computer science, the Davis–Putnam–Logemann–Loveland (DPLL) algorithm is a complete, backtracking-based search algorithm for deciding the satisfiability of propositional logic formulae in conjunctive normal form, i.e. for solving the CNF-SAT problem.
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