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Towards a Formal Treatment of VLSI Arrays

Johnsson, Lennart and Weiser, Uri and Cohen, Danny and Davis, Alan L. (1981) Towards a Formal Treatment of VLSI Arrays. In: Proceedings of the Second Caltech Conference on Very Large Scale Integration. California Institute of Technology , Pasadena, CA, pp. 375-398. http://resolver.caltech.edu/CaltechCONF:20120508-133029898

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Abstract

This paper presents a formalism for describing the behavior of computational networks at the algorithmic level. It establishes a direct correspondence between the mathematical expressions defining a function and the computational networks which compute that function. By formally manipulating the symbolic expressions that define a function, it is possible to obtain different networks that compute the function. From this mathematical description of a network, one can directly determine certain important characteristics of computational networks, such as computational rate, performance and communication requirements. The use of this formalism for design and verification is demonstrated on computational networks for Finite Impulse Response (FIR} filters, matrix operations, and the Discrete Fourier Transform (DFT). The progression of computations can often be modeled by wave fronts in an illuminating way. The formalism supports this model. A computational network can be viewed in an abstract form that can be represented as a graph. The duality between the graph representation and the mathematical expressions is briefly introduced.


Item Type:Book Section
Additional Information:The authors gratefully acknowledge the support for this research provided generously by the Defense Advanced Research Projects Agency, under contracts MDA-SG-C-0523 with the USC/Information Sciences Institute and N0001 4-79-C-0597 with the California Institute of Technology, and by the Burroughs Corporation for the Data Driven Research Project at the University of Utah. Views and conclusions contained in this paper are the authors' and should not be interpreted as representing the official opinion or policy of DARPA, the U.S. Government, any person or agency connected with them, nor of the Burroughs Corporation.
Funders:
Funding AgencyGrant Number
Defense Advanced Research Projects AgencyMD-80-C-0523
Defense Advanced Research Projects AgencyN00014-79-C-0597
Burroughs CorporationUNSPECIFIED
Record Number:CaltechCONF:20120508-133029898
Persistent URL:http://resolver.caltech.edu/CaltechCONF:20120508-133029898
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:230
Collection:CaltechCONF
Deposited By: Kristin Buxton
Deposited On:06 Aug 2012 23:03
Last Modified:26 Dec 2012 07:11

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