Search results
Results from the WOW.Com Content Network
In this case, unit propagation is performed based on the literals of the partial model, and unit clauses are removed if their literal is in the model. In the example above, the unit clause a {\displaystyle a} would be added to the partial model; the simplification of the set of clauses would then proceed as above with the difference that the ...
A clause is a disjunction of literals (or a single literal). A clause is called a Horn clause if it contains at most one positive literal. 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 NP-completeness of NAE3SAT can be proven by a reduction from 3-satisfiability (3SAT). [2] First the nonsymmetric 3SAT is reduced to the symmetric NAE4SAT by adding a common dummy literal to every clause, then NAE4SAT is reduced to NAE3SAT by splitting clauses as in the reduction of general -satisfiability to 3SAT.
Algorithm DP SAT solver Input: A set of clauses Φ. Output: A Truth Value: true if Φ can be satisfied, false otherwise. function DP-SAT(Φ) repeat // unit propagation: while Φ contains a unit clause {l} do for every clause c in Φ that contains l do Φ ← remove-from-formula(c, Φ); for every clause c in Φ that contains ¬l do Φ ← remove-from-formula(c, Φ); Φ ← add-to-formula(c ...
MAX-SAT is one of the optimization extensions of the boolean satisfiability problem, which is the problem of determining whether the variables of a given Boolean formula can be assigned in such a way as to make the formula evaluate to TRUE. If the clauses are restricted to have at most 2 literals, as in 2-satisfiability, we get the MAX-2SAT ...
In mathematical logic, a literal is an atomic formula (also known as an atom or prime formula) or its negation. [1] [2] The definition mostly appears in proof theory (of classical logic), e.g. in conjunctive normal form and the method of resolution. Literals can be divided into two types: [2] A positive literal is just an atom (e.g., ).
Get AOL Mail for FREE! Manage your email like never before with travel, photo & document views. Personalize your inbox with themes & tabs. You've Got Mail!
Boolean algebra An area of algebra in which the values of the variables are the truth values true and false, typically used in computer science, logic, and mathematical logic. Boolean negation A form of negation where the negation of a non-true proposition is true, and the negation of a non-false proposition is false. [34] [35] [36] Boolean ...