Simultaneous decompositions of sequential machines
TL;DR: The theoretical and practical results that were obtained in the field of simultaneous decompositions which divide the process described by a given sequential machine into a number of interacting parallel partial processes, each implemented by one partial machine are described.
About: This article is published in Microprocessing and Microprogramming.The article was published on 1990-08-01. It has received 18 citations till now. The article focuses on the topics: Field (computer science).
Citations
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TL;DR: The fundamentals of a logic design methodology which meets the requirements of today's complex circuits and modem building blocks are presented and the decomposition methodology that is presented ensures “correctness by construction” and enables very effective and efficient post-factum validation.
Abstract: Modem microelectronic technology.gives opportunities to build digital circuits of huge complexity and provides a wide diversity of logic building blocks. Although logic designers have been building circuits for many years, they have realized that advances in microelectronic technology are outstripping their abilities to make use of the created opportunities. In this paper, we present the fundamentals of a logic design methodology which meets the requirements of today's complex circuits and modem building blocks. The methodology is based on the theory of general full-decompositions which constitutes the theory of digital circuit structures at the highest abstraction level. The paper explains the theory and shows how it can be used for digital circuit synthesis. The decomposition methodology that is presented ensures “correctness by construction” and enables very effective and efficient post-factum validation. It makes possible extensive examination of the structural features of the required information processing in relation to a given set of objectives and constraints.
46 citations
Cites background from "Simultaneous decompositions of sequ..."
...parallel full-decompositions [19]-[27], in which each of the component machines can compute its own next-state and output independently (Fig....
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...7); serial full-decompositions [22]-[27], in which only one of the component machines (Me) uses information from the second machine (M1) in order to compute its own next-state and output (Fig....
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...tions with state and input, state or input information transmitted), and on the type of coding/decoding (symbol or bit coding/decoding) [22]-[27]....
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...9); bitfull-decompositions [25]-[27], where the decod-...
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01 Sep 1997
TL;DR: The fundamental apparatus for the analysis and evaluation of information relationships is introduced and explained, which forms a complete information modeling and analysis apparatus that can be applied in logic design, decision system design, pattern recognition, knowledge discovery, machine learning and other areas.
Abstract: The analysis of information relationships is of primary importance for the analysis and synthesis of digital information systems. The paper aims to introduce and discuss the fundamental apparatus for the analysis and evaluation of information relationships. It defines and explains various relationships between information, measures for the amount and importance of information, and measures for the strength and importance of the information relationships. It demonstrates importance of the introduced relationships and measures for efficient synthesis, and shows how to apply them in the synthesis process. The analysis apparatus makes operational the famous theory of partitions and set systems of Hartmanis (1966). While partitions and set systems enable one to model information, the relationships and measures enable one to analyze and measure information and information relationships. Both together form a complete information modeling and analysis apparatus that can be applied in logic design, decision system design, pattern recognition, knowledge discovery, machine learning and other areas.
39 citations
16 Mar 1992
TL;DR: The objective of the new decomposition method is to implement a complex Boolean function or an assigned sequential machine with a minimal number of constrained building blocks and minimal connections between the blocks to solve problems with hard constraints in multiple dimensions.
Abstract: Since today's complex digital systems and circuits are difficult to design, optimize, implement and verify, decomposition methods and tools have attracted great interest recently. The objective of the new decomposition method presented in this paper is to implement a complex Boolean function or an assigned sequential machine with a minimal number of constrained building blocks and minimal connections between the blocks. The method aims in solving problems with hard constraints in multiple dimensions for which, to the authors' knowledge, no solution has yet been published. It differs substantially from the methods for solving similar simpler one-dimensional problems. The method is very general and, after some small changes, it can be applied to many other partitioning problems. The experimental results show that the method is very efficient. >
29 citations
01 Sep 2003
TL;DR: A new sequential circuit synthesis methodology is discussed that targets LUT FPGAs and FPGA-based reconfigurable system-on-a-chip platforms and demonstrates that the information-driven approach consistently applied in the whole sequential Circuit synthesis chain efficiently produces very fast and compact sequential circuits.
Abstract: Reconfigurable systems fill the flexibility, performance, power dissipation, and development and fabrication cost gap between the application specifc systems implemented with hard-wired application specific integrated circuits and systems based on the standard (general purpose) programmable microprocessors. During the last decade they became the mainstream implementation technology for custom computation and embedded system products in such fields as telecommunication, image processing, video processing, multimedia, DSP, cryptography, embedded control, etc. To efficiently develop, implement and use the reconfigurable systems, adequate computer-aided support tools are necessary. Since most reconfigurable systems are implemented using the look-up table (LUT) field programmable gate arrays (FPGA) technology, the circuit synthesis tools targeting this technology are of primary importance for their effective and efficient implementation. In this paper, a new sequential circuit synthesis methodology is discussed that targets LUT FPGAs and FPGA-based reconfigurable system-on-a-chip platforms. The methodology is based on the information-driven approach to circuit synthesis, general decomposition and theory of information relationship measures that we previously developed. Our synthesis methods considerably differ from all other known methods. The experimental results from the automatic circuit synthesis tools that implement our methods demonstrate that the information-driven approach consistently applied in the whole sequential circuit synthesis chain efficiently produces very fast and compact sequential circuits.
25 citations
TL;DR: A heuristic method is presented for suboptimal multiple-objective sequential general decomposition of sequential machines into submachines with limited input/output bits, product terms and state variables and shows that it is efficient and flexible.
22 citations
References
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TL;DR: This paper studies the problem of replacing (decomposing) a complex finite state sequential machine by several simpler ones which operate in parallel and yield the same result.
Abstract: In this paper we study the problem of replacing (decomposing) a complex finite state sequential machine by several simpler ones which operate in parallel and yield the same result. In the first part, we give the necessary mathematical background and results. In the second part, we apply these results and derive the necessary and sufficient conditions for the existence of a decomposition for a given machine. If a decomposition exists then the required simpler machines which have to be connected in parallel are given.
60 citations
01 Jan 1989
TL;DR: It is proved, that the bit full- decomposition can be treated as a special case of the symbol full-decomposition; therefore, no new decomposition theory is needed for this case, but the symbolFulldecompositions theory together with the theorems introduced here constitute the theory of bitFullDecomposition.
Abstract: Control units and serial processing units of today's information processing systems must realize complex processes, which are usually described in the form of a sequential machine or a number of cooperating sequential machines. Large machines are difficult to: design, optimize, implement and verify. Therefore, there is a real need for CAD tools, which could decompose a complex sequential machine into a number of smaller and less complicated partial machines. For many years, the decomposition of only the internal states of sequential machines has been studied. However, this sort of decomposition is not a sUfficient solution. The complexity of a circuit implementing a sequential machine is a function not only of machine's internal states but as well of inputs and outputs. Furthermore, the possibility to implement a machine with today's array logic building blocks depends not only on the number of internal states but as well on inputs and outputs. So, there is a real need for decompositions upon the states, inputs and outputs of a sequential machine, i.e. for fulldecompositions. During the full-decomposition process, the input and/or state and/or output symbols (values) can be decomposed or the input and/or state and/or output bits. So, it is possible to perform the symbol fulldecomposition or the bit full-decomposition. This report provides the classification of full-decompositions and describes briefly the theoretical foundations of bit fulldecomposition. Comparing to the symbol full-decomposition,the bit fulldecomposition has the following advantage: input and output decoders are reduced to an appropriate distribution of the primary input and output bits between the partial machines. In the report, definitions of a bit partition and bit partition pairs are introduced and their usefulness to bit full-decompositions is shown. It is proved, that the bit full-decomposition can be treated as a special case of the symbol full-decomposition; therefore, no new decomposition theory is needed for this case, but the symbol fulldecomposition theory together with the theorems introduced here constitute the theory of bit full-decomposition. Finally, a comparison is made between the symbol and the bit fulldecompositions and some practical conclusions and remarks are presented. In the appendix, an example is provided that illustrates the possibility and the practical usefulness of bit full-decomposition. Based on the developed theory, the CAD algorithms calculating different bit full-decompositions have been developed and implemented. Those algorithms and the practical results are presented and estimated in the separate paper [5]. Index Terms Automata theory, decomposition, logic design, sequential machines. Acknowledgements The author is indebted to Prof. ir. A. Heetman and Prof. ir. M. P.J. Stevens for making it possible to perform this work, to Dr. P.R. Attwood for making corrections to the English text and to mr. C. van de Watering for typing the text.
19 citations
01 Jan 1989
TL;DR: A special full-decomposition strategy is investigated, which has several advantages comparing to the case where a sequential machine is considered as a unit, and can be directly used in order to develope programs computing different sorts of decompositions for sequential machines.
Abstract: The decomposition theory of sequential machines aims to find answers to the following important practical problem: how to decompose a complex sequential machine into a number of simpler partial machines in order to: simplify the design, implementation and verification process; make it possible to process (to optimize, to implement, to test, ••. ) the separate partial machines al though it may be impossible to process the whole machine with existing tools; make it possible to implement the machine with existing building blocks or inside of a limited silicon area. For many years, decomposition of the internal states of sequential machines has been investigated. Here, decomposition of the states, as well as, the inputs and outputs of sequential machines is considered, i.e. full-decomposition. In [16], classification of full-decompositions is presented and theorems about the existence of different full-decompositions are provided. In this report a special full-decomposition strategy is investigated the full-decomposition of sequential machines with the separate realization of the next-state and output functions. This strategy has several advantages comparing to the case where a sequential machine is considered as a unit. In the report, the results of theoretical investigations are presented; however, the notions and theorems provided here have straightforward practical interpretations and they can be directly used in order to develope programs computing different sorts of decompositions for sequential machines. INDEX TERMS Automata theory, decomposition, logic system design, sequential machines. ACKNOWLEDGEMENTS The author is indebted to Prof. ir. A. Heetman and Prof. ir. M. P.J. Stevens for making it possible to perform this work, to Dr. P.R. Attwood for making corrections to the English text and to mr. C. van de Watering for typing the text.
17 citations
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