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Preface

Published online by Cambridge University Press:  01 June 2011

Yves Crama
Affiliation:
Université de Liège, Belgium
Peter L. Hammer
Affiliation:
Rutgers University, New Jersey
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Summary

Boolean functions, meaning {0,1}-valued functions of a finite number of {0,1}-valued variables, are among the most fundamental objects investigated in pure and applied mathematics. Their importance can be explained by several interacting factors.

  • It is reasonable to argue that a multivariate function f:A1×A2×…×AnA is “interesting” only if each of the sets A1,A2,…,An, and A contains at least two elements, since otherwise the function either depends trivially on some of its arguments, or is constant. Thus, in a sense, Boolean functions are the “simplest interesting” multivariate functions. It may even be surprising, actually, that such primitive constructs turn out to display a rich array of properties and have been investigated by various breeds of scientists for more than 150 years.

  • When the arguments of a Boolean function are viewed as atomic logical propositions, the value of the function at a 0–1 point can be interpreted as the truth value of a sentence composed from these propositions. Carrying out calculation son Boolean functions is then tantamount to performing related logical operations (such as inference or theorem-proving) on propositional sentences. Therefore, Boolean functions are at the heart of propositional logic.

  • […]

Type
Chapter
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Boolean Functions
Theory, Algorithms, and Applications
, pp. xv - xviii
Publisher: Cambridge University Press
Print publication year: 2011

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  • Preface
  • Yves Crama, Université de Liège, Belgium, Peter L. Hammer, Rutgers University, New Jersey
  • Book: Boolean Functions
  • Online publication: 01 June 2011
  • Chapter DOI: https://doi.org/10.1017/CBO9780511852008.001
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  • Preface
  • Yves Crama, Université de Liège, Belgium, Peter L. Hammer, Rutgers University, New Jersey
  • Book: Boolean Functions
  • Online publication: 01 June 2011
  • Chapter DOI: https://doi.org/10.1017/CBO9780511852008.001
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Preface
  • Yves Crama, Université de Liège, Belgium, Peter L. Hammer, Rutgers University, New Jersey
  • Book: Boolean Functions
  • Online publication: 01 June 2011
  • Chapter DOI: https://doi.org/10.1017/CBO9780511852008.001
Available formats
×