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 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.
Keywords
Preview
Unable to display preview. Download preview PDF.
References
Barreiro, N., Ehrhard, T.: Anatomy of an extensional collapse. Submittend paper. (1997). Available from http://hypatia.dcs.qmw.ac.uk/cgi-bin/sarah?q=ehrhard.
Berger, U.: Total Objects and Sets in domain Theory. Annals of Pure and Applied Logic 60 (1993) 91–117
Boppana, R. B., Sipser, M.: The Complexity of finite functions. In: van Leeuwen, J. (ed.): Handbook of Theoretical Computer Science, vol. A. Elsevier (1990) 759–802
Bucciarelli, A.: Logical Reconstruction of Bi-Domains. Proc. of the 3rd Int. Conf. on Typed Lambda Calculi and Applications, LNCS 1210, Springer-Verlag (1997) 99–111
Ehrhard, T.: A relative definability result for strongly stable functions, and some corollaries. (1997) To appear in Information and Computation. Available from http://hypatia.dcs.qmw.ac.uk/cgi-bin/sarah?q=ehrhard.
Mitchell, J. C.: Type Systems for Programming Languages. In: van Leeuwen, J. (ed.): Handbook of Theoretical Computer Science, vol. B, Elsevier (1990) 365–458
Plotkin, G.: LCF considered as a programming language. Theoretical Computer Science 5 (1997) 223–256
Plotkin, G.: Full Abstraction, Totality and PCF. Available from http://hypatia.dcs.qmw.ac.uk/authors/P/PlotkinGD/
Sazonov, V. Y.: Degrees of Parallelism in Computations. Proc. Conference on Mathematical Foundations of Computer Science, LNCS 45, Springer-Verlag (1976)
Wegener, I.: The Complexity of Boolean functions. Wiley-Teubner Series in Comp. Sci., New York-Stutgart (1987)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1998 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bucciarelli, A., Salvo, I. (1998). Totality, definability and boolean circuits. In: Larsen, K.G., Skyum, S., Winskel, G. (eds) Automata, Languages and Programming. ICALP 1998. Lecture Notes in Computer Science, vol 1443. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0055104
Download citation
DOI: https://doi.org/10.1007/BFb0055104
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-64781-2
Online ISBN: 978-3-540-68681-1
eBook Packages: Springer Book Archive