Totality, definability and boolean circuits

  • Antonio Bucciarelli
  • Ivano Salvo
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1443)


In the type frame originating from the flat domain of boolean values, we single out elements which are hereditarily total. We show that these elements can be defined, up to total equivalence, by sequential programs. The elements of an equivalence class of the totality equivalence relation (totality class) can be seen as different algorithms for computing a given set-theoretic boolean function. We show that the bottom element of a totality class, which is sequential, corresponds to the most eager algorithm, and the top to the laziest one. Finally we suggest a link between size of totality classes and a well known measure of complexity of boolean functions, namely their sensitivity.


Logical Relations Scott's Model PCF Boolean Circuits 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Antonio Bucciarelli
    • 1
  • Ivano Salvo
    • 1
  1. 1.Dipartimento di Scienze dell'InformazioneUniversité di Roma “La Sapienza”RomeItaly

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