Abstract
The computer calculation of values of Boolean functions and systems of Boolean functions represented by normal polynomial forms starts from calculating values of terms of this polynomial followed by operations performed over the results. For the classical calculation method, this process is sequential. In this work, an algorithm is given that uses no more than one logical operation and one comparison to calculate the values of disjunctive and conjunctive terms of polynomial forms.
Similar content being viewed by others
References
Malyugin, V.D. and Sokolov, V.V., Intensive Logic Computations, Avtom. Telemekh., 1993, no. 4, pp. 160–167.
Zakrevskii, A.D., Pottosin, Yu.V., and Cheremisinova, L.D., Logicheskie osnovy proektirovaniya diskretnykh ustroistv (Logic Fundamentals of Discrete Device Design), Moscow: FIZMATLIT, 2007.
Pukhal’skii, G.I. and Novosel’tseva, T.Ya., Tsifrovye ustroistva: Uchebnoe posobie dlya VTUZov (Digital Devices: A Tutorial for Institutes of Higher Technical Education), St. Petersburg: Politekhnika, 1996.
Malyugin, V.D., Parallel’nye logicheskie vychisleniya posredstvom arifmeticheskikh poli-nomov (Parallel Logic Computations by Arithmetic Polynomials), Moscow: Nauka, 1997.
Vykhovanets, V.S., Signal Treatment in Discrete Bases on the Base of Generalized Polynomial Forms, Doklady 2-i mezhdunarodnoi konferentsii “Tsifrovaya obrabotka signalov i ee primenenie” (Proc. 2nd Int. Conf. ‘Digital Treatment of Signals and Its Application’), Moscow, 1999, vol. 2, pp. 372–377.
Fin’ko, O.A., Modulyarnaya arifmetika parallel’nykh logicheskikh vychislenii (Module Arithmetic of Parallel Logic Computations) Malyugin, V.D., Ed., Moscow: Inst. Probl. Upravl., 2003
Fomichev, V.M., Diskretnaya matematika i kriptologiya: Kurs lektsii, (Discrete Mathematics and Cryptology. Course of Lectures), Podufalov, N.D., Ed., Moscow: Dialog-Mos. Inzh. Fiz. Inst., 2003.
Shalyto, A.A., Logicheskoe upravlenie. Metody apparatnoi i programmnoi realizatsii algoritmov (Logic Management. Methods of Hardware and Software Realization of Algorithms), St. Petersburg: Nauka, 2000.
Sizonenko, A.B., High Performance Algorithm of Computation of Nonlinear Arithmetic Polynomial Terms by Serial Computational Technique Means, in Sbornik nauchnykh trudov po materialam mezhdunarodnoi nauchnoprakticheskoi konferentsii “Sovremennye prob-lemy i puti ikh resheniya v nauke, transporte, proizvodstve i obrazovanii 2010” (Collection of Papers on the Base of Proc. Int. Sci.-Pract. Conf. ‘Contemporary Problems and Ways of Their Solution in Science, Transport, Industry and Education’) Odessa: Chernomor’e, 2010, pp. 35–38.
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © A.B. Sizonenko, 2012, published in Avtomatika i Vychislitel’naya Tekhnika, 2012, No. 4, pp. 5–16.
About this article
Cite this article
Sizonenko, A.B. A high-performance algorithm for calculating conjunctive and disjunctive terms in polynomial representations of Boolean functions. Aut. Control Comp. Sci. 46, 147–156 (2012). https://doi.org/10.3103/S0146411612040062
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S0146411612040062