Linearly definable classes of boolean functions

Miguel Couceiro, Erkko Lehtonen

Research output: Contribution to journalConference articlepeer-review

1 Citation (Scopus)
14 Downloads (Pure)


In this paper we address the question “How many properties of Boolean functions can be defined by means of linear equations?” It follows from a result by Sparks that there are countably many such linearly definable classes of Boolean functions. In this paper, we refine this result by completely describing these classes. This work is tightly related with the theory of function minors and stable classes, a topic that has been widely investigated in recent years by several authors including Maurice Pouzet.

Original languageEnglish
Pages (from-to)21-28
Number of pages8
JournalCEUR Workshop Proceedings
Publication statusPublished - 2020
Event1st International Conference "Algebras, Graphs and Ordered Sets", ALGOS 2020 - Virtual, Online
Duration: 26 Aug 202028 Aug 2020


  • Boolean function
  • Clone
  • Clonoid
  • Functional equation
  • Linear definability


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