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Boolean Computation—Wolfram Language Documentation

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• Functions
  • AllTrue
  • And
  • AnyTrue
  • BitAnd
  • BitLength
  • BitOr
  • BitSet
  • BitShiftLeft
  • BitXor
  • Boole
  • BooleanConsecutiveFunction
  • BooleanConvert
  • BooleanCountingFunction
  • BooleanFunction
  • BooleanMaxterms
  • BooleanMinimize
  • BooleanMinterms
  • BooleanTable
  • BooleanVariables
  • CellularAutomaton
  • Conjunction
  • Disjunction
  • Equivalent
  • Exists
  • False
  • FindClusters
  • ForAll
  • HammingDistance
  • Implies
  • LogicalExpand
  • Majority
  • MatchingDissimilarity
  • Maximize
  • Minimize
  • Nand
  • Nearest
  • NoneTrue
  • Nor
  • Not
  • Or
  • Resolve
  • RulePlot
  • SatisfiabilityCount
  • SatisfiabilityInstances
  • SatisfiableQ
  • ShiftRegisterSequence
  • SubstitutionSystem
  • TautologyQ
  • True
  • TuringMachine
  • UnateQ
  • Xnor
  • Xor
• Related Guides
  • Discrete Mathematics
  • Bitwise Operations
  • Basic Logic & Boolean Algebra
• Tech Notes
  • Relational and Logical Operators
  • Solving Logical Combinations of Equations

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.

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

True, False — symbolic truth values

Boole — convert symbolic truth values to 0 and 1

BooleanCountingFunction — out of variables true

BooleanConsecutiveFunction — consecutive out of variables true

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. ∑, ∏)

AllTrue  ▪  AnyTrue  ▪  NoneTrue

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)

RulePlot — visualize a Boolean function

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

BooleanMinimize — find a minimal Boolean form

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

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

Resolve — eliminate quantified variables from a Boolean expression

LogicalExpand — expand expressions involving Boolean operators and equations

CellularAutomaton  ▪  TuringMachine  ▪  SubstitutionSystem  ▪  ShiftRegisterSequence

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

Nearest, FindClusters — operate on Boolean vectors

HammingDistance  ▪  MatchingDissimilarity  ▪  ...

Minimize, Maximize — Boolean optimization

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