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Berechnungen in partiellen Algebren endlichen Typs

Computational complexity in partial algebras of finite type

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Zusammenfassung

Die Methode von Shannon und Lupanov, den minimalen Schaltaufwand zur Darstellung einer typischen Wahrheitsfunktion durch ein logisches Netz nach unten abzuschätzen, wird auf Berechnungen in partiellen Algebren endlichen Typs verallgemeinert. Die Arbeit enthält Anwendungen auf freie Gruppen, Polynomringe über endlichen Körpern, Boolesche Ringe und die approximative Berechnung von reellen Zahlen.

Abstract

The method of Shannon and Lupanov to estimate the minimal size of a logical net for the representation of a typical truth function is generalized to computations in partial algebras of finite type. Applications are given to free groups, polynomial rings over finite fields, Boolean rings and to the approximate computation of real numbers.

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Authors and Affiliations

  1. Seminar für Angewandte Mathematik Universität Zürich, Freiestrasse 36, CH-8032, Zürich, Schweiz

    V. Strassen

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  1. V. Strassen
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Strassen, V. Berechnungen in partiellen Algebren endlichen Typs. Computing 11, 181–196 (1973). https://doi.org/10.1007/BF02252909

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  • DOI: https://doi.org/10.1007/BF02252909