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Equation variables, including Y0 - Y9, r1 - r6, and u, v, w. These are essentially strings which store equations. They are evaluated to return a value when used in an expression or program. Specific values, (constant, C) can be plugged in for the independent variable (X) by following the equation name (dependent, Y) by the constant value in ...
Suppose that a 2-satisfiability instance contains two clauses that both use the same variable x, but that x is negated in one clause and not in the other. Then the two clauses may be combined to produce a third clause, having the two other literals in the two clauses; this third clause must also be satisfied whenever the first two clauses are ...
¬P(X) in the first clause, and in non-negated form P(a) in the second clause. X is an unbound variable, while a is a bound value (term). Unifying the two produces the substitution X ↦ a. Discarding the unified predicates, and applying this substitution to the remaining predicates (just Q(X), in this case), produces the conclusion: Q(a)
For example, x 1 is a positive literal, ¬x 2 is a negative literal, and x 1 ∨ ¬x 2 is a clause. The formula (x 1 ∨ ¬x 2) ∧ (¬x 1 ∨ x 2 ∨ x 3) ∧ ¬x 1 is in conjunctive normal form; its first and third clauses are Horn clauses, but its second
For each clause c in C, let S + c and S − c denote the sets of variables which are not negated in c, and those that are negated in c, respectively. The variables y x of the ILP will correspond to the variables of the formula F, whereas the variables z c will correspond to the clauses. The ILP is as follows:
In computer science and formal methods, a SAT solver is a computer program which aims to solve the Boolean satisfiability problem.On input a formula over Boolean variables, such as "(x or y) and (x or not y)", a SAT solver outputs whether the formula is satisfiable, meaning that there are possible values of x and y which make the formula true, or unsatisfiable, meaning that there are no such ...
As an example, the clause A(X):-X>0,B(X) is a clause containing the constraint X>0 in the body. Constraints can also be present in the goal. The constraints in the goal and in the clauses used to prove the goal are accumulated into a set called constraint store. This set contains the constraints the interpreter has assumed satisfiable in order ...
Clauses of length q are converted to length 3 by adding new (auxiliary) variables e.g. x 2 ∨ x 10 ∨ x 11 ∨ x 12 = ( x 2 ∨ x 10 ∨ y R) ∧ ( y R ∨ x 11 ∨ x 12). This requires a maximum of q2 q 3-SAT clauses. If z ∈ L then there is a proof π such that V π (z) accepts for every R i. All clauses are satisfied if x i = π(i) and ...