Wolfram Language & System 12.0 (2019)|Legacy Documentation

This is documentation for an earlier version of Wolfram Language.View current documentation (Version 14.1)

BooleanConsecutiveFunction

represents a Boolean function of n variables that gives True if k consecutive variables are True.

treats the variable list as cyclic.

BooleanConsecutiveFunction[{k₁,k₂,…,k_d},{n₁,n₂,…,n_d}]

represents a Boolean function of n₁ n₂ ⋯ n_d variables that gives True if all variables in a block of the variable array are True.

BooleanConsecutiveFunction[{{k₁,k₂,…,k_d},{c₁,c₂,…,c_d}},{n₁,n₂,…,n_d}]

treats the i level of the variable array as cyclic if c_i is True.

gives the Boolean expression in variables a_i corresponding to the Boolean consecutive function specified by spec.

BooleanConsecutiveFunction[spec,{a₁,a₂,…},form]

gives the Boolean expression in the form specified by form.

BooleanConsecutiveFunction[k,n] is also known as linear consecutive-k-out-of-n:F.
BooleanConsecutiveFunction[{k,True},n] is also known as circular consecutive-k-out-of-n:F.
BooleanConsecutiveFunction[{k,False},n] is equivalent to BooleanConsecutiveFunction[k,n].
BooleanConsecutiveFunction[{{k₁,k₂,…,k_d},c},{n₁,n₂,…,n_d}] is equivalent to BooleanConsecutiveFunction[{{k₁,k₂,…,k_d},{c,c,…,c}},{n₁,n₂,…,n_d}].
BooleanConsecutiveFunction[spec] gives a Boolean function object that works like Function.
BooleanConsecutiveFunction[spec][a₁,a₂,…] gives an implicit representation equivalent to the explicit Boolean expression BooleanConsecutiveFunction[spec,{a₁,a₂,…}].
In BooleanConsecutiveFunction[…,{n₁,n₂,…,n_d},…][vars], vars can be either an array of dimension-{n₁,n₂,…,n_d} variables, or a list of n₁ n₂ ⋯ n_d variables.
In BooleanConsecutiveFunction[{k₁,k₂,…,k_d},vars], vars needs to be a depth-d array of variables.
BooleanConvert converts BooleanConsecutiveFunction[spec][vars] to an explicit Boolean expression.
In BooleanConsecutiveFunction[spec,vars,form], the possible forms are as given for BooleanConvert.
BooleanConsecutiveFunction[spec,vars] by default gives an expression in disjunctive normal form (DNF).