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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 ...
A formula is in conjunctive normal form (CNF) if it is a conjunction of clauses (or a single clause). For example, x 1 is a positive literal, ¬x 2 is a negative literal, and x 1 ∨ ¬x 2 is a clause.
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 ...
The Boolean satisfiability problem on conjunctive normal form formulas is NP-complete. By the duality principle, so is the falsifiability problem on DNF formulas. Therefore, it is co-NP-hard to decide if a DNF formula is a tautology. Conversely, a DNF formula is satisfiable if, and only if, one of its conjunctions is satisfiable.
The "2" in this name stands for the number of literals per clause, and "CNF" stands for conjunctive normal form, a type of Boolean expression in the form of a conjunction of disjunctions. [1] They are also called Krom formulas, after the work of UC Davis mathematician Melven R. Krom, whose 1967 paper was one of the earliest works on the 2 ...
Together with the normal forms in propositional logic (e.g. disjunctive normal form or conjunctive normal form), it provides a canonical normal form useful in automated theorem proving. Every formula in classical logic is logically equivalent to a formula in prenex normal form.
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 ...