But it can take exponential time and space to convert a general SAT problem to disjunctive normal form; for an example exchange "'" " and " ( " " in the above exponential blow-up example for conjunctive normal forms.
22.
For propositional satisfiability of conjunctive normal form formulae, which is the original settings of this algorithm, every such a move changes the value of the variable from true to false or vice versa, and produce the satisfiability of the violated constraint.
23.
Since all logical formulae can be converted into an equivalent formula in conjunctive normal form, proofs are often based on the assumption that all formulae are CNF . However, in some cases this conversion to CNF can lead to an exponential explosion of the formula.
24.
:" Technically, the propositional function has been reduced to its ( unminimized ) conjunctive normal form : each row has its minterm expression and these can be OR'd to produce the formula in its ( unminimized ) conjunctive normal form ."
25.
:" Technically, the propositional function has been reduced to its ( unminimized ) conjunctive normal form : each row has its minterm expression and these can be OR'd to produce the formula in its ( unminimized ) conjunctive normal form ."
26.
SNP contains " k "-SAT, the boolean satisfiability problem ( SAT ) where the formula is restricted to conjunctive normal form and to at most " k " literals per clause, where " k " is fixed.
27.
A positive function of a given system of variables, that uses all of its variables, is read-once if and only if every prime implicant of the disjunctive normal form and every clause of the conjunctive normal form have exactly one variable in common.
28.
In this problem, we have a boolean formula in conjunctive normal form where each variable appears at most 3 times, and we wish to know the maximum number of clauses that can be simultaneously satisfied by a single assignment of true / false values to the variables.
29.
The existence of negation normal forms drives many applications, for example in digital circuit design, where it is used to manipulate the types of logic gates, and in formal logic, where it is needed to find the conjunctive normal form and disjunctive normal form of a formula.
30.
In the maximum-2-satisfiability problem ( "'MAX-2-SAT "'), the input is a formula in conjunctive normal form with two literals per clause, and the task is to determine the maximum number of clauses that can be simultaneously satisfied by an assignment.
