Abstract
This paper is dedicated to two seemingly different problems. The first one concerns information systems theory and the second one is connected to logic synthesis methods. The common aspect in considering these problems together is the important task of the economic representation of data in information systems and as well as in logic systems. An efficient algorithm to solve the task of attributes/arguments reduction as well as functional decomposition of decision/truth tables is presented. In the latter case a new technique is suggested, which decomposes the original decision/ truth table into an equivalent set of subtables. Using manipulations based on both rough sets and Boolean algebra theory, the decision table is reduced and decomposed so as to get an efficient implementation.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Brayton R.K.,Hachtel G.D.,McMullen C.T., Sangiovanni-Vincentelli A. (1984) Logic Minimization Algorithms for VLSI Synthesis. Kluwer Academic Publ.
Brown F.M., (1990). Boolean Reasoning. The Logic of Boolean Equations. Kluwer Academic Publ.
Fang K., Wójcik A.S., (1988). Modular Decomposition of Combinational Multiple-Valued Circuits. IEEE Trans. on Computers, vol 37,No. 10, 1293–1301
Grzymala-Busse J.W. and Pawlak Z.,(1984).On Some Subset of the Partition Set.Fundamenta Informaticae VII.3, 483–488.
Hartmanis J. and Stearns R.E.,(1966). Algebraic Structure Theory of Sequential Machines. Prentice—Hall.
Hurley R.B.,(1983). Decision Tables in Software Engineering. Van Nostrand Reinhold Company, New York.
Jasinski K., Luba T., Kalinowski J.,(1989). Parallel Decomposition in Logic Synthesis. Proc.l5th European Solid-State Circuits Conf.,113–116.
Jasinski K., Luba T., Kalinowski J.,(1991). CAD Tools for PLD Implementation of ASICs. Proc. of Second Eurochip Workshop on VLSI Design Training,Grenoble, 225–230.
Luba T., (1986). A Uniform Method of Boolean Function Decomposition. Rozprawy Elektrotechniczne (Journal of the Polish Academy of Science), No. 4, 1041–1054.
Luba T., Kalinowski J., Jasinski K., Krasniewski A., (1991). Combining Serial Decomposition with Topological Partitioning for Effective Multi-Level PLA Implementations. In Logic and Architecture Synthesis, P.Michel and G.Saucier (Editors), Elsevier Science Publishers B. V. (North-Holland).
Luba T., Kalinowski J., Jasinski K., (1991). PLATO: A CAD Tool for Logic Synthesis Based on Decomposition. Proc. of European Conference on Design Automation, 65–69.
Luba T., Janowski J., Rybnik J., (1991). Relations Between Multiple-Valued Logic and Decision Logic with Respect to Rough Set Theory Semantic. Research Report, Institute of Teclecommunications.No.39.
Luba T., Markowski M.A., Zbierzchowski B., (1992). Logic Decomposition for Programmable Gate Arrays. Proc. of Euro-ASIC’92, Paris (to appear).
McCluskey E.J., (1986). Logic Design Principles. With Emphasis on Testable Semicustom Circuits. Prentice—Hall.
Pawlak Z., (1983),Informations Systems. Theoretical Foundations.(in Polish) WNT.
Pawlak Z., (1991). Rough Sets. Theoretical Aspects of Reasoning about Data. Kluwer Academic Publishers.
Rudell R.L, Sangiovanni-Vincentelli A.,(1987). Multiple-Valued Minimization for PLA Optimization. IEEE Transactions on Computer—Aided Design.
Rybnik J.,(1990). Minimizations of Partially Defined Switching Functions Using Rough Sets Theory. Manuscript.
Sasao T.,(1989). On the Optimal Design of MultipleValued PLA’s. IEEE Trans. on Computers, Vol.38, No. 4, 582–592.
Sasao T.,(1988). Multiple—Valued Logic and Optimization of Programmable Logic Arrays. Computer.
Sasao T.,(1984). Input Variable Assignment and Output Phase Optimization of PLA’s. IEEE Transactions on Computers.
Skowron A. and Rauszer C., (1991). The Discernibility Matrices and Functions in Information Systems. ICS Report., Institute of Computer Science.l.
Varma D., Trachtenberg E.A.,(1989). Design Automation Tools for Efficient Implementation of Logic Functions by Decomposition. IEEE Trans. on CAD 8, No. 8, 901–916.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1992 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Łuba, T., Rybnik, J. (1992). Rough Sets and Some Aspects of Logic Synthesis. In: Słowiński, R. (eds) Intelligent Decision Support. Theory and Decision Library, vol 11. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-7975-9_13
Download citation
DOI: https://doi.org/10.1007/978-94-015-7975-9_13
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4194-4
Online ISBN: 978-94-015-7975-9
eBook Packages: Springer Book Archive