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A model of computation for VLSI with related complexity results

Authors:

Bernard Chazelle,

Louis MonierAuthors Info & Claims

STOC '81: Proceedings of the thirteenth annual ACM symposium on Theory of computing

Pages 318 - 325

https://doi.org/10.1145/800076.802485

Published: 11 May 1981 Publication History

Abstract

We propose a new model of computation for VLSI which is a refinement of previous models and makes the additional assumption that the time for propagating information is linear in the distance. Our approach is motivated by the failure of previous models to allow for realistic asymptotic analysis. While accommodating for basic laws of physics, this model tries to be most general and technology-independent. Thus, from a complexity viewpoint, it is especially suited for deriving lower bounds and trade-offs. We present new results for a number of problems including fan-in, addition, transitive functions, matrix multiplication, and sorting.

References

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G.M. Baudet, On the Complexity of VLSI Circuits: A New Tool, INRIA 1981, to appear.

[2]

R.P. Brent and H.T. Kung, The Chip Complexity of Binary Arithmetic, proc. 12th Annual ACM Symposium on Theory of Computing, ACM, pp. 190-200, May 1980.

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[3]

G.M. Baudet, F.P. Preparata and J. Vuillemin, Area-Time Optimal VLSI Circuits for Convolution, Rapport INRIA # 30, Rocquencourt France, 1980.

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W.A. Clark, From Electron Mobility to Logical Structure: A View of Integrated Circuits, Computing Surveys, Vol.12, No 3, September 1980.

Digital Library

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B.M. Chazelle and L.M. Monier, Towards More Realistic Models of Computation for VLSI, proc. of Caltech Conference on VLSI, January 1981.

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H.T. Kung and C.E. Leiserson, Systolic Arrays for (VLSI), appeared in {MC80}.

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C. Mead and L. Conway, Introduction to VLSI Systems, Addison-Wesley, 1980.

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F.P. Preparata and J. Vuillemin, The Cube-Connected-Cycles: A Versatile Network for Parallel Computation, proc. 20th Annual Symposium on Foundations of Computer Science, Oct. 1979.

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F.P. Preparata and J. Vuillemin, Area-Time Optimal VLSI Networks based on the Cube-Connect Cycles, Rapport IRIA # 13, Rocquencourt France, 1980.

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C.D. Thompson, Area-Time Complexity for VLSI, proc. 11th Annual ACM Symposium on Theory of Computing, ACM, pp. 81-88, May 1979.

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C.D. Thompson, A Complexity Theory for VLSI, Ph.D. dissertation, Department of Computer Science, Carnegie-Mellon University, 1980.

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J. Vuillemin, A Combinatorial Limit to the Computing Power of V.L.S.I. Circuits, proc. 21st Annual Symposium on Foundations of Computer Science, Oct. 1980.

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Cited By

Chen RPark NPrasanna V(2013)High throughput energy efficient parallel FFT architecture on FPGAs2013 IEEE High Performance Extreme Computing Conference (HPEC)10.1109/HPEC.2013.6670343(1-6)Online publication date: Sep-2013
https://doi.org/10.1109/HPEC.2013.6670343
Wada KHagihara KTokura N(2007)Area‐time complexity on a vlsi model with boundary layout assumptionSystems and Computers in Japan10.1002/scj.469017060817:6(67-75)Online publication date: 21-Mar-2007
https://doi.org/10.1002/scj.4690170608
Kahrs M(2006)Silicon compilation of very high level languageIEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems10.1109/43.17098711:10(1227-1246)Online publication date: 1-Nov-2006
https://dl.acm.org/doi/10.1109/43.170987
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A model of computation for VLSI with related complexity results

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cover image ACM Conferences

STOC '81: Proceedings of the thirteenth annual ACM symposium on Theory of computing

May 1981

390 pages

ISBN:9781450373920

DOI:10.1145/800076

Copyright © 1981 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

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Publication History

Published: 11 May 1981

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Cited By

Chen RPark NPrasanna V(2013)High throughput energy efficient parallel FFT architecture on FPGAs2013 IEEE High Performance Extreme Computing Conference (HPEC)10.1109/HPEC.2013.6670343(1-6)Online publication date: Sep-2013
https://doi.org/10.1109/HPEC.2013.6670343
Wada KHagihara KTokura N(2007)Area‐time complexity on a vlsi model with boundary layout assumptionSystems and Computers in Japan10.1002/scj.469017060817:6(67-75)Online publication date: 21-Mar-2007
https://doi.org/10.1002/scj.4690170608
Kahrs M(2006)Silicon compilation of very high level languageIEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems10.1109/43.17098711:10(1227-1246)Online publication date: 1-Nov-2006
https://dl.acm.org/doi/10.1109/43.170987
Dehne FSack J(2005)A survey of parallel computational geometry algorithmsParcella '8810.1007/3-540-50647-0_104(73-88)Online publication date: 2-Jun-2005
https://doi.org/10.1007/3-540-50647-0_104
Aggarwal ACarter JKosaraju S(2005)Optimal tradeoffs for addition on systolic arraysVLSI Algorithms and Architectures10.1007/3-540-16766-8_6(57-69)Online publication date: 1-Jun-2005
https://doi.org/10.1007/3-540-16766-8_6
Rosenberg A(2005)The VLSI revolution in theoretical circlesAutomata, Languages and Programming10.1007/3-540-13345-3_2(23-40)Online publication date: 28-May-2005
https://doi.org/10.1007/3-540-13345-3_2
Hagihara KWada KTokura N(2005)Effects of practical assumption in area complexity of VLSI computationRIMS Symposia on Software Science and Engineering10.1007/3-540-11980-9_20(128-146)Online publication date: 1-Jun-2005
https://doi.org/10.1007/3-540-11980-9_20
Jang JPark HPrasanna V(1997)An Optimal Multiplication Algorithm on Reconfigurable MeshIEEE Transactions on Parallel and Distributed Systems10.1109/71.5982788:5(521-532)Online publication date: 1-May-1997
https://dl.acm.org/doi/10.1109/71.598278
Ghouse M(1993)2D grid architectures for the DFT and the 2D DFTJournal of VLSI signal processing systems for signal, image and video technology10.1007/BF018802725:1(57-74)Online publication date: 1-Jan-1993
https://doi.org/10.1007/BF01880272
Feldman YShapiro E(1992)Spatial machinesCommunications of the ACM10.1145/135239.13524235:10(60-73)Online publication date: 1-Oct-1992
https://dl.acm.org/doi/10.1145/135239.135242
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