article

Free access

A model of computation for VLSI with related complexity results

Authors:

Bernard Chazelle,

Louis MonierAuthors Info & Claims

Journal of the ACM (JACM), Volume 32, Issue 3

Pages 573 - 588

https://doi.org/10.1145/3828.3834

Published: 01 July 1985 Publication History

Abstract

A new model of computation for VLSI, based on the assumption that time for propagating information is at least linear in the distance, is proposed. While accommodating for basic laws of physics, the model is designed to be general and technology independent. Thus, from a complexity viewpoint, it is especially suited for deriving lower bounds and trade-offs. New results for a number of problems, including fan-in, transitive functions, matrix multiplication, and sorting are presented. As regards upper bounds, it must be noted that, because of communication costs, the model clearly favors regular and pipelined architectures (e.g., systolic arrays).

References

[1]

BAUDET, G. M.On the area required by VLSI circuits. In VLSI Systems and Computations, H. T. Kung, R. Sproull, and G. Steele, Eds. Computer Science Press, Rockville, Md., 1981, pp. 100-107.

[2]

BAUDET, G. M., PREPARATA, F. P., AND VUILLEMIN, J. Area-time optimal VLSI circuits for convolution. 1EEE Trans. Comput. C-32, 7 (July 1983), 684-688.

[3]

BILARDI, G., PRACCHI, M., AND PREPARATA, F. P. A critique of network speed in VLSI models of computation. IEEE J. Solid-State Circuits SC-I 7 (Aug. 1982), 696-702.

[4]

BRENT, R. P., AND KUNG, H. T.The chip complexity of binary arithmetic. In Proceedings ofl 2th Annual ACM Symposium on Theory of Computing (Los Angeles, Calif., Apr. 28-30). ACM, New York, 1980, pp. 190-200.

[5]

CHAZELLE, B., AND MONIER, L.Towards more realistic models of computation for VLSI. In Proceedings of2nd Caltech Conference on VLSI (Pasadena, Calif., Jan. 19-21). 1981, pp. 441-453.

[6]

CLARK, W. A. From electron mobility to logical structure: A view of integrated circuits. ACM Comput. Surv. 12, 3 (Sept. 1980), 325-358.

[7]

KEDEM, Z. M., AND ZORAT, A.On relations between input and communication/computation in VLSI. In Proceedings of 22nd IEEE Symposium on Foundations of Computer Science. IEEE, New York, 1981, pp. 37-44.

[8]

KUNG, H. T., AND LEISERSON, C. E.Systolic arrays (for VLSI). In introduction to VLSI Systems, C. Mead and L. Conway, Eds. Addison-Wesley, Reading, Mass., 1980.

[9]

LIPTON, R. J., AND SEDGEWICK, R.Lower bounds for VLSI. In Proceedings of l3th Annual ACM Symposium on Theory of Computing (Milwaukee, Wis., May 11-13). ACM, New York, 1981, pp. 300-307.

[10]

LIPTON, R. J., AND VALDES, J.Census functions: An approach to VLSI upper bounds, in Proceedings of 22nd IEEE Symposium on Foundations of Computer Science. IEEE, New York, 1981, pp. 13-22.

[11]

MEAD, C., AND CONWAY, L., EDS.Introduction to VLSI Systems. Addison-Wesley, Reading, Mass., 1980.

[12]

PREPARATA, F. P., AND VUILLEMIN, J.Area-time optimal VLSI networks based on the cubeconnected cycles. Rapport IRIA No. 13, Rocquencourt, France, 1980.

[13]

PREPARATA, F. P., AND VUILLEMIN, J.The cube-connected cycles: A versatile network for parallel computation. Commun. ACM 24, 5 (May 1981), 300-309.

[14]

ROSENBERG, A. L.Three-dimensional VLSI: A case study. J. ACM 30, 3 (July 1983), 397-416.

[15]

SAVAGE, J. E.Area-time tradeoffs for matrix multiplication and related problems in VLSI models. J. Comput. Syst. Sci. ( 1981 ), 230-242.

[16]

SEITZ, C. L. Self-timed VLSI Systems. In Proceedings of Ist Caltech Conference on VLSI (Pasadena, Calif., Jan.). 1979.

[17]

THOMPSON, C. D.Area-time complexity for VLSI. In Proceedings 11th Annual ACM Symposium on Theory of Computing (Atlanta, Ga., Apr. 30-May 2). ACM, New York, 1979, pp. 81-88.

[18]

THOMPSON, C. D. A Complexity Theory for VLSI. PhD dissertation, Dept. of Computer Science, Carnegie-Mellon Univ., Pittsburgh, Pa., 1980.

[19]

THOMPSON, C. D.Fourier Transforms in VLSI. IEEE Trans. Comput. C-32, 1I (Nov. 1983), 1047-1057.

[20]

VUILLEMtN, J.A combinatorial limit to the computing power of VLSI circuits. IEEE Trans. Comput. C-32, 3 (Mar. 1983), 294-300.

Cited By

Lozhkin SZizov V(2024)Asymptotically sharp estimates for the area of multiplexers in the cellular circuit modelDiscrete Mathematics and Applications10.1515/dma-2024-000934:2(103-115)Online publication date: 15-Apr-2024
https://doi.org/10.1515/dma-2024-0009
Lozhkin SZizov V(2022)Асимптотически точные оценки для площади мультиплексоров в модели клеточных схемAsymptoticaly tight bounds for the area of multiplexers in a cellular circuit modelДискретная математикаDiskretnaya Matematika10.4213/dm171234:4(52-68)Online publication date: 2-Dec-2022
https://doi.org/10.4213/dm1712
Modanese A(2021)Lower Bounds and Hardness Magnification for Sublinear-Time Shrinking Cellular AutomataComputer Science – Theory and Applications10.1007/978-3-030-79416-3_18(296-320)Online publication date: 28-Jun-2021
https://dl.acm.org/doi/10.1007/978-3-030-79416-3_18
Show More Cited By

Index Terms

A model of computation for VLSI with related complexity results
1. Hardware
  1. Very large scale integration design
2. Theory of computation
  1. Models of computation

Recommendations

A model of computation for VLSI with related complexity results
STOC '81: Proceedings of the thirteenth annual ACM symposium on Theory of computing

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 ...
A VLSI Modulo m Multiplier

A novel method to compute the exact digits of the modulo m product of integers is proposed, and a modulo m multiply structure is defined. Such a structure can be implemented by means of a few fast VLSI binary multipliers, and a response time of about ...
Vlsi array design and fast numerical computation

Comments

Information & Contributors

Information

Published In

cover image Journal of the ACM

Journal of the ACM Volume 32, Issue 3

July 1985

245 pages

ISSN:0004-5411

EISSN:1557-735X

DOI:10.1145/3828

Issue’s Table of Contents

Copyright © 1985 ACM.

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 July 1985

Published in JACM Volume 32, Issue 3

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Qualifiers

Article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

44
Total Citations
View Citations
516
Total Downloads

Downloads (Last 12 months)52
Downloads (Last 6 weeks)11

Reflects downloads up to 02 Sep 2024

Other Metrics

View Author Metrics

Citations

Cited By

Lozhkin SZizov V(2024)Asymptotically sharp estimates for the area of multiplexers in the cellular circuit modelDiscrete Mathematics and Applications10.1515/dma-2024-000934:2(103-115)Online publication date: 15-Apr-2024
https://doi.org/10.1515/dma-2024-0009
Lozhkin SZizov V(2022)Асимптотически точные оценки для площади мультиплексоров в модели клеточных схемAsymptoticaly tight bounds for the area of multiplexers in a cellular circuit modelДискретная математикаDiskretnaya Matematika10.4213/dm171234:4(52-68)Online publication date: 2-Dec-2022
https://doi.org/10.4213/dm1712
Modanese A(2021)Lower Bounds and Hardness Magnification for Sublinear-Time Shrinking Cellular AutomataComputer Science – Theory and Applications10.1007/978-3-030-79416-3_18(296-320)Online publication date: 28-Jun-2021
https://dl.acm.org/doi/10.1007/978-3-030-79416-3_18
Mitra SWong HWong S(2015)The Trojan-proof chipIEEE Spectrum10.1109/MSPEC.2015.702451152:2(46-51)Online publication date: 1-Feb-2015
https://dl.acm.org/doi/10.1109/MSPEC.2015.7024511
Wisnioski M(2015)The birth of innovationIEEE Spectrum10.1109/MSPEC.2015.702451052:2(40-61)Online publication date: 27-Jan-2015
https://dl.acm.org/doi/10.1109/MSPEC.2015.7024510
Denison TMorris MSun F(2015)Building a bionic nervous systemIEEE Spectrum10.1109/MSPEC.2015.702450952:2(32-39)Online publication date: 27-Jan-2015
https://dl.acm.org/doi/10.1109/MSPEC.2015.7024509
Smil V(2015)It's too soon to judge shale gas [Numbers Don't Lie]IEEE Spectrum10.1109/MSPEC.2015.702450552:2(28-28)Online publication date: 27-Jan-2015
https://dl.acm.org/doi/10.1109/MSPEC.2015.7024505
Patel P(2015)Profile: CyPhy Works [Resources_Start-Ups]IEEE Spectrum10.1109/MSPEC.2015.702450452:2(27-27)Online publication date: 27-Jan-2015
https://dl.acm.org/doi/10.1109/MSPEC.2015.7024504
Courtland R(2015)Review: The Uncanny Valley [Resources_Review]IEEE Spectrum10.1109/MSPEC.2015.702450352:2(26-26)Online publication date: 27-Jan-2015
https://dl.acm.org/doi/10.1109/MSPEC.2015.7024503
Dern D(2015)Wrangling digital pictures [Resources_Tools]IEEE Spectrum10.1109/MSPEC.2015.702450252:2(25-25)Online publication date: 1-Feb-2015
https://dl.acm.org/doi/10.1109/MSPEC.2015.7024502
Show More Cited By

View Options

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

Get Access

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Article

Media

Figures

Other

Tables

View Issue’s Table of Contents