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EQUISATISFIABILITY

Equisatisfiability

values of two equisatisfiable formulae may nevertheless disagree for a particular assignment of variables. As a result, equisatisfiability differs from

Equisatisfiability

Logical equivalence

Concept in logic

same truth value. Philosophy portal Psychology portal Entailment Equisatisfiability If and only if Logical biconditional Logical equality ≡ the iff symbol

Logical equivalence

Logical_equivalence

Tseytin transformation

Operation in Boolean circuit theory

variables introduced. While this is redundant, it does not affect the equisatisfiability of the resulting equation. Now substitute each gate with its appropriate

Tseytin transformation

Tseytin_transformation

Boolean satisfiability problem

Problem of determining if a Boolean formula could be made true

variables. However, with use of the Tseytin transformation, we may find an equisatisfiable conjunctive normal form formula with length linear in the size of the

Boolean satisfiability problem

Boolean_satisfiability_problem

Skolem normal form

Formalism of first-order logic

formula is not necessarily equivalent to the original one, but is equisatisfiable with it: it is satisfiable if and only if the original one is satisfiable

Skolem normal form

Skolem_normal_form

Rewriting

Replacing subterm in a formula with another term

rewriting systems in logic may not preserve truth values, see e.g. equisatisfiability. Term rewriting systems can be employed to compute arithmetic operations

Rewriting

Modal clausal form

Normal form for modal logic formulas

normal modal logic, any set of formulae can be transformed into an equisatisfiable set of formulae in this normal form. In multimodal logic where a represents

Modal clausal form

Modal_clausal_form

Higher-order logic

Formal system of logic

sense that for every formula of a higher-order logic, one can find an equisatisfiable formula for it in second-order logic. The term "higher-order logic"

Higher-order logic

Higher-order_logic

Conjunctive normal form

Standard form of Boolean function

means that the original formula and the result of the translation are equisatisfiable but not equivalent. An alternative translation, the Tseitin transformation

Conjunctive normal form

Conjunctive_normal_form

Conflict-driven clause learning

SAT solving algorithm

C} , is called the resolvent of the two clauses. The resolvent is equisatisfiable with its premises (that is, the resolvent is satisfiable if and only

Conflict-driven clause learning

Conflict-driven_clause_learning

XOR-SAT

input clause with more than 3 literals can be transformed into an equisatisfiable conjunction of clauses á 3 literals similar to above; i.e. XOR-SAT

XOR-SAT

Witness (mathematics)

Input value for which an existential statement of a function is true

, y ) {\displaystyle \forall x\,\exists y\,\varphi (x,y)} then an equisatisfiable statement for S is ∃ f ∀ x φ ( x , f ( x ) ) {\displaystyle \exists

Witness (mathematics)

Witness_(mathematics)

Davis–Putnam algorithm

Check the validity of a logic formula

each step of the SAT solver, the intermediate formula generated is equisatisfiable, but possibly not equivalent, to the original formula. The resolution

Davis–Putnam algorithm

Davis–Putnam_algorithm

Game semantics

Approach to formal semantics

ϕ ( x , y ) {\displaystyle \forall x\exists y\,\phi (x,y)} then an equisatisfiable statement for S is ∃ f ∀ x ϕ ( x , f ( x ) ) {\displaystyle \exists

Game semantics

Game_semantics

1-in-3-SAT

NP-complete variant of the Boolean satisfiability problem

3-SAT instance with m clauses and n variables may be converted into an equisatisfiable one-in-three 3-SAT instance with 5m clauses and n + 6m variables. The

1-in-3-SAT