Research on "Semantics and Logics of Computation"

Totality, Definability and Boolean Circuits

ABSTRACT. 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 the 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.

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BIBTEX.

@conference{bucciarelli-salvo:00,
   author    = {A. Bucciarelli and I. Salvo},
   title     = {Totality, Definability and Boolean Circuits},
   booktitle = {{Proceedings of 25th ICALP}},
   year      = {1998},
   publisher = {Springer},
   volume    = {1443},
   pages     = {808--819},
   series    = {LNCS},
}