Building on its core symbolic architecture, the Wolfram Language gives immediate access to the latest in industrial-strength Boolean computation. With highly general symbolic representations of Boolean functions, with full support for "don't-care" arguments and values, the Wolfram Language provides state-of-the-art Boolean function transformation, minimization, elimination, satisfiability, and analysis, making possible verification, testing, and other applications involving hundreds to hundreds of thousands of variables.

Basic Boolean Operators

And (&& ,∧ )  ▪ Or (|| ,∨ )  ▪ Not (! ,¬ )  ▪ Nand (⊼ )  ▪ Nor (⊽ )  ▪ Xor (⊻ ) ▫ Xnor ( )  ▪ Implies ( )  ▪ Equivalent (⧦ )  ▪ Majority

True , False — symbolic truth values

Boole — convert symbolic truth values to 0 and 1

Special Boolean Functions

BooleanCountingFunction — out of variables true

BooleanConsecutiveFunction — consecutive out of variables true

General Boolean Functions

BooleanFunction — general Boolean function (from IDs, mappings with "don't cares", ...)

BooleanMinterms , BooleanMaxterms — combinations of minterms, maxterms

Conjunction , Disjunction — AND, OR with respect to a list of variables (cf. ∑, ∏)

Predicates on Lists

AllTrue   ▪ AnyTrue   ▪ NoneTrue

Boolean Structure

BooleanTable — create a truth vector or general truth table

BooleanVariables — find the variables in a Boolean expression

UnateQ — test whether a Boolean expression is unate (monotone)

Visualization

RulePlot — visualize a Boolean function

Conversion & Minimization

BooleanConvert — convert to a specified format (CNF, DNF, ESOP, NOR, BFF, ...)

BooleanMinimize — find a minimal Boolean form

Boolean Function Testing

SatisfiableQ — test whether any input to a function can give True

SatisfiabilityCount — count how many possible inputs give True

SatisfiabilityInstances — find instances of inputs that give True

TautologyQ — test whether all possible inputs give True

Predicate Calculus

ForAll (∀ ), Exists (∃ ) — quantify over Boolean variables

Resolve — eliminate quantified variables from a Boolean expression

LogicalExpand — expand expressions involving Boolean operators and equations

Iterated Boolean Systems »

CellularAutomaton   ▪ TuringMachine   ▪ SubstitutionSystem   ▪ ShiftRegisterSequence

Bit Vector Operations »

BitAnd   ▪ BitOr   ▪ BitXor   ▪ BitLength   ▪ BitShiftLeft   ▪ BitSet   ▪ ...

Numerical Boolean Computation

Nearest , FindClusters — operate on Boolean vectors

HammingDistance   ▪ MatchingDissimilarity   ▪ ...

Minimize , Maximize — Boolean optimization