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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 ...
For some versions of the SAT problem, it is useful to define the notion of a generalized conjunctive normal form formula, viz. as a conjunction of arbitrarily many generalized clauses, the latter being of the form R(l 1,...,l n) for some Boolean function R and (ordinary) literals l i. Different sets of allowed Boolean functions lead to ...
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 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.
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 ...
As there exist polynomial-time algorithms to convert any Boolean expression to conjunctive normal form such as Tseitin's algorithm, posing SAT problems in CNF does not change their computational difficulty. SAT problems are canonically expressed in CNF because CNF has certain properties that can help prune the search space and speed up the ...
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 ...
Configuration file, in computing, typically with file extension .cnf, .conf, .cfg, .cf, or .ini Conjunctive normal form , also known as clausal normal form, in Boolean logic Constant weight without fins , a freediving discipline in which usage of fins or change of ballast is prohibited