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Journal ArticleDOI

Trinity algebra and its application ot machine decompositions

23 Nov 1987-Information Processing Letters (Elsevier North-Holland, Inc.)-Vol. 26, Iss: 3, pp 127-134
TL;DR: Partition trinity and trinity algebra efficiently give the information dependence between inputs, states, and outputs within a triple of partitions, and they serve as a powerful tool to the full-decompositions of machines.
About: This article is published in Information Processing Letters.The article was published on 1987-11-23. It has received 12 citations till now.
Citations
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Journal ArticleDOI
TL;DR: Theoreme mettant en œuvre une methode de decomposition, d'une comprehension plus aisee que le theoreme de Krohn Rhodes as mentioned in this paper.
Abstract: Presentation d'un theoreme mettant en œuvre une methode de decomposition, d'une comprehension plus aisee que le theoreme de Krohn Rhodes
01 Mar 1988
TL;DR: In this work, a general and unified classification of full-decompositions for Mealy and Moore machines are presented and some theorems about the existence ofFull-decoms with the output behaviour realization are formulated and proved and constitute a theoretical basis for the practical decomposition algorithms and for the software system calculating different sorts of decomposition for sequential machines.
Abstract: The control units of large digital systems can use up to 80% of the entire hardware implementing the system. Therefore, it is very important to reduce the amount of hardware taken by the control unit and to simplify the design, implementation and verification process. In most cases, the control unit can be constructed as a sequential machine. In this work, a general and unified classification of full-decompositions and formal definitions of different sorts of full-decompositions for Mealy and Moore machines are presented and some theorems about the existence of full-decompositions with the output behaviour realization are formulated and proved. This theorems constitute a theoretical basis for the practical decomposition algorithms and for the software system calculating different sorts of decomposition for sequential machines.
References
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Book
01 Jan 1982
TL;DR: In this paper, the holonomy decomposition is used to decompose semigroups and their relatives into machines and semiggroups, and their relation to semigroup decompositions.
Abstract: Introduction 1 Semigroups and their relatives 2 Machines and semigroups 3 Decompositions 4 The holonomy decomposition 5 Recognizers 6 Sequential machines and functions Appendix References Index of notation Index

174 citations

Book
01 Jan 1986
TL;DR: Part 1 Principles of logic systems: Combinational logic logic and memory devices combinational logic at different levels of integration synchronous sequential circuits asynchronous sequential circuits arithmetic logic circuits and advanced logic systems.
Abstract: Part 1 Principles of logic systems: combinational logic logic and memory devices combinational logic at different levels of integration synchronous sequential circuits asynchronous sequential circuits arithmetic logic circuits. Part 2 Advanced logic systems: combinational logic techniques partitioning of sequential circuits partition-based design for synchronous sequential circuits partition-based design for asynchronous sequential circuits hybrid design techniques for sequential circuits CAD of logic circuits.

64 citations

01 Jan 1986
TL;DR: The final author version and the galley proof are versions of the publication after peer review that features the final layout of the paper including the volume, issue and page numbers.
Abstract: • A submitted manuscript is the version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers.

9 citations

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Partition trinity and trinity algebra efficiently give the information dependence between inputs, states, and outputs within a triple of partitions, and they serve as a powerful tool to the full-decompositions of machines.