Search results
Results from the WOW.Com Content Network
To find the value of the Boolean function for a given assignment of (Boolean) values to the variables, we start at the reference edge, which points to the BDD's root, and follow the path that is defined by the given variable values (following a low edge if the variable that labels a node equals FALSE, and following the high edge if the variable ...
A law of Boolean algebra is an identity such as x ∨ (y ∨ z) = (x ∨ y) ∨ z between two Boolean terms, where a Boolean term is defined as an expression built up from variables and the constants 0 and 1 using the operations ∧, ∨, and ¬. The concept can be extended to terms involving other Boolean operations such as ⊕, →, and ≡ ...
A Boolean value is either true or false. A Boolean expression may be composed of a combination of the Boolean constants True/False or Yes/No, Boolean-typed variables, Boolean-valued operators, and Boolean-valued functions. [1] Boolean expressions correspond to propositional formulas in logic and are a special case of Boolean circuits. [2]
Boole's expansion theorem, often referred to as the Shannon expansion or decomposition, is the identity: = + ′ ′, where is any Boolean function, is a variable, ′ is the complement of , and and ′ are with the argument set equal to and to respectively.
In Boolean algebra, any Boolean function can be expressed in the canonical disjunctive normal form , [1] minterm canonical form, or Sum of Products (SoP or SOP) as a disjunction (OR) of minterms. The De Morgan dual is the canonical conjunctive normal form ( CCNF ), maxterm canonical form , or Product of Sums ( PoS or POS ) which is a ...
Simplification is the process of replacing a mathematical expression by an equivalent one that is simpler (usually shorter), according to a well-founded ordering. Examples include: Simplification of algebraic expressions, in computer algebra; Simplification of boolean expressions i.e. logic optimization
The satisfiability problem becomes more difficult if both "for all" and "there exists" quantifiers are allowed to bind the Boolean variables. An example of such an expression would be ∀x ∀y ∃z (x ∨ y ∨ z) ∧ (¬x ∨ ¬y ∨ ¬z); it is valid, since for all values of x and y, an appropriate value of z can be found, viz. z=TRUE if ...
In Boolean algebra, a formula is in conjunctive normal form (CNF) or clausal normal form if it is a conjunction of one or more clauses, where a clause is a disjunction of literals; otherwise put, it is a product of sums or an AND of ORs.