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
More filters
01 Jan 1988
TL;DR: A general and unified classification of full decompositions is presented, formal definitions of different sorts of full-decompositions for Mealy and Moore machines are introduced and theorems about the existence of fulldecomPOSitions with the state and output behaviour realization are formulated and proved.
Abstract: The design of large logic systems leads to the practical problem how to decompose a complex system into a number of simpler subsystems. The decomposition theory of sequential machines tries to find answers to this problem for sequential machines. For many years, the "simpler" machine was defined as a machine with fewer states and, therefore, state-decompositions of sequential machines were considered. Together with the progress in LSI technology and the introduction of array logic into the design of sequential circuits a real need arose for decompositions not only on states of sequential machines but on inputs and outputs too, i.e. for full-decompositions. In this report, a general and unified classification of fulldecompositions is presented, formal definitions of different sorts of full-decompositions for Mealy and Moore machines are introduced and theorems about the existence of fulldecompositions with the state and output behaviour realization are formulated and proved. The presented theorems have a straightforward practical interpretation. Based on them, a set of algorithms has been developed and a system of programs has been made for computing the different sorts of decompositions.
14 citations
Cites methods from "Trinity algebra and its application..."
...An approach to the full-decomposition of sequential machines has been presented in [14) and [15]....
[...]
01 Jan 1989
TL;DR: In this paper, the authors present a general full-decomposition of type PO ••••••••••••••• and a serial fulldecompositions of type NS •••••• •.
Abstract: CONTENTS 1. Introduction. . • • . . • • • • • • • • • • • . • • • • • • • • • • • • • • • • • • . • • • . •• 2 2. Full-decompositions and their sorts .••••••••••••••••••• 4 3. Partitions, partition pairs and partition trinities •••• 14 4. Parallel full-decomposition •••••••••••••••••••••••••••• 17 5. Serial full-decomposition of type PS ••••••••.•••••••••• 19 6. Serial full-decomposition of type NS ••••••••••.•••••••• 22 7. Serial full-decomposition of type PO ••••••••••••••••••• 26 8. Serial full-decomposition of type NO ••••••••••••••••••• 29 9. General full-decomposition of type PS •••••••••••••••••• 33 10. General full-decomposition of type PO •••••••.•••.•.•••• 35 11. Conclusion ••..•.•.••••••••.••..••..•••.••.••••••••••.•• 37
11 citations
TL;DR: This paper examines the algebraic structure of a system's actions and finds that these actions often possess a self-similar local neighborhood structure that permits analysis and synthesis to be performed locally yet produce global, intelligent behaviours.
Abstract: Artificial Intelligence focuses on the question of how to design system to exhibit intelligent behaviour in complex environments. Complex global behaviours can emerge from simple systems acting in a complex environment; however, this emergence requires that the systems' internal structure reflect essential structures in the environment. This paper examines the algebraic structure of a system's actions. We find that these actions often possess a self-similar local neighborhood structure that permits analysis and synthesis to be performed locally yet produce global, intelligent behaviours. A procedure for finding this local structure is presented, and illustrated with examples.
11 citations
Cites methods from "Trinity algebra and its application..."
...Hou(1987) , Ito(1981), Topolskiy(1979), and Zimmer(1990)....
[...]
...…has been used extensively in previous attempts to automate hierarchical synthesis by finding a wreath product decomposition of a given system, e.g. Agibalov & Evtushenko(1984), Arbib & Manes(1974), Evtushenko(1979), Halatsis et al.(1978), Hou(1987), Ito(1981), Topolskiy(1979), and Zimmer(1990)....
[...]
25 Aug 2004
TL;DR: This paper suggests and compares several tie-breaking policies for deadline-based schedule algorithms on multiprocessor and identifies an effective tie- Breaking policy for different scheduling algorithm by simulation.
Abstract: Real-time scheduling on multiprocessor involves many complex issues. One of them is tie-breaking: the way how ties are broken among tasks with same priority. Unlike on uniprocessor, the feasibility of a task set on multiprocessor depends on a tie-breaking policy as well as on a scheduling algorithm. In this paper, we suggest and compare several tie-breaking policies for deadline-based schedule algorithms on multiprocessor. An effective tie-breaking policy for different scheduling algorithm is identified by simulation.
8 citations
TL;DR: It is found that a system's actions often possess a self-similar local neighbourhood structure that permits analysis and synthesis to be performed locally and yet produces global intelligent behaviours.
Abstract: Artificial intelligence focuses on the question of how to design systems to exhibit intelligent behaviour in complex environments. Complex global behaviours can emerge from simple systems acting in a complex environment; however, this emergence requires that the systems' internal structure reflects essential structures in the environment This paper examines the algebraic structure of a system's actions. We find that these actions often possess a self-similar local neighbourhood structure that permits analysis and synthesis to be performed locally and yet produces global intelligent behaviours. A procedure for finding this local structure is presented and illustrated with examples.
7 citations
References
More filters
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