BooleanMaxterms

BooleanMaxterms[k,n]

represents the k^(th) maxterm in n variables.

BooleanMaxterms[{k1,k2,…},n]

represents the conjunction of the maxterms ki.

BooleanMaxterms[{{u1,…,un},{v1,…},…}]

represents the conjunction of maxterms given by the exponent vectors ui, vi, ….

BooleanMaxterms[spec,{a1,a2,…}]

gives the Boolean expression in variables ai corresponding to the maxterms function specified by spec.

BooleanMaxterms[spec,{a,a2,…},form]

gives the Boolean expression in the form specified by form.

Details

  • BooleanMaxterms[{{u1,u2,…}},{a1,a2,…}] gives b1∨b2∨… where bi==ai if ui is True and bi=¬ai if ui is False.
  • The ui etc. can be either True and False or 1 and 0.
  • BooleanMaxterms[k,n] is equivalent to BooleanMaxterms[{IntegerDigits[k,n,2]}].
  • BooleanMaxterms[spec] gives a Boolean function object that works like Function.
  • BooleanMaxterms[spec][a1,a2,…] gives an implicit representation equivalent to the explicit Boolean expression BooleanMaxterms[spec,{a1,a2,…}].
  • BooleanConvert converts BooleanMaxterms[spec][vars] to an explicit Boolean expression.
  • In BooleanMaxterms[spec,{a1,a2,…},form], the possible forms are as given for BooleanConvert.
  • BooleanMaxterms[spec,{a1,a2,…}] by default gives an expression in CNF.

Examples

open allclose all

Basic Examples  (4)

Equivalent ways of specifying the same maxterm:

Specify a conjunction of maxterms:

An equivalent way to specify a conjunction of maxterms:

Return a BooleanFunction object representing the conjunction of maxterms:

Enumerate all maxterms of three variables:

Scope  (1)

Specify different forms for the result:

Applications  (1)

Produce a CNF formula for ∏(1,3,5):

Properties & Relations  (4)

The indices correspond to positions of False, in the default ordering for BooleanTable:

BooleanMaxterms can represent any BooleanFunction:

The mapping from maxterms to index:

The mapping from index to maxterms:

Using bit vectors:

Use Subsets to enumerate all possible Boolean functions using BooleanMaxterms:

BooleanMinterms is related to BooleanMaxterms:

Wolfram Research (2008), BooleanMaxterms, Wolfram Language function, https://reference.wolfram.com/language/ref/BooleanMaxterms.html.

Text

Wolfram Research (2008), BooleanMaxterms, Wolfram Language function, https://reference.wolfram.com/language/ref/BooleanMaxterms.html.

CMS

Wolfram Language. 2008. "BooleanMaxterms." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/BooleanMaxterms.html.

APA

Wolfram Language. (2008). BooleanMaxterms. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/BooleanMaxterms.html

BibTeX

@misc{reference.wolfram_2024_booleanmaxterms, author="Wolfram Research", title="{BooleanMaxterms}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/BooleanMaxterms.html}", note=[Accessed: 26-April-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_booleanmaxterms, organization={Wolfram Research}, title={BooleanMaxterms}, year={2008}, url={https://reference.wolfram.com/language/ref/BooleanMaxterms.html}, note=[Accessed: 26-April-2024 ]}