Article

Efficient computation of canonical form for Boolean matching in large libraries

Authors:

Debatosh Debnath,

Tsutomu SasaoAuthors Info & Claims

ASP-DAC '04: Proceedings of the 2004 Asia and South Pacific Design Automation Conference

Pages 591 - 596

Published: 27 January 2004 Publication History

Abstract

This paper presents an efficient technique for solving a Boolean matching problem in cell-library binding, where the number of cells in the library is large. As a basis of the Boolean matching, we use the notion NP-representative (NPR); two functions have the same NPR if one can be obtained from the other by a permutation and/or complementation(s) of the variables. By using a table look-up and a tree-based breadth-first search strategy, our method quickly computes NPR for a given function. Boolean matching of the given function against the whole library is determined by checking the presence of its NPR in a hash table, which stores NPRs for all the library functions and their complements. The effectiveness of our method is demonstrated through experimental results, which shows that it is more than two orders of magnitude faster than the Hinsberger-Kolla's algorithm---the fastest Boolean matching algorithm for large libraries.

References

[1]

L. Benini and G. De Micheli, "A survey of Boolean matching techniques for library binding." ACM Trans. Design Automation of Electronic Systems, vol. 2, no. 3, pp. 193--226, July 1997.

Digital Library

[2]

J. R. Burch and D. E. Long, "Efficient Boolean function matching," in Proc. IEEE/ACM Int. Conf. on Computer-Aided Design, pp. 408--411, Nov. 1992.

Digital Library

[3]

J. Ciric and C. Sechen, "Efficient canonical form for Boolean matching of complex functions in large libraries," IEEE Trans. Computer-Aided Design of Integrated Circuits and Systems, vol. 22, no. 5, pp. 535--544, May 2003.

Digital Library

[4]

E. M. Clarke, K. L. McMillan, X. Zhao, M. Fujita, and J. Yang, "Spectral transforms for large Boolean functions with applications to technology mapping," Formal Methods in System Design: An Int. Journal, vol. 10, no. 2, pp. 137--148, Apr. 1997.

Digital Library

[5]

D. Debnath and T. Sasao, "A heuristic algorithm to design AND-OR-EXOR three-level networks," in Proc. Asia and South Pacific Design Automation Conf., pp. 69--74, Feb. 1998.

[6]

D. Debnath and T. Sasao, "Fast Boolean matching under permutation using representative," in Proc. Asia and South Pacific Automation Conf., pp. 359--362, Jan. 1999.

[7]

G. De Micheli, Synthesis and Optimization of Digital Circuits, McGraw-Hill, 1994.

Digital Library

[8]

S. Ercolani and G. De Micheli, "Technology mapping for electrically prorammable gate arrays," in Proc. IEEE/ACM Design Automation Conf., pp. 234--239, June 1991.

Digital Library

[9]

M. A. Harrison, Introduction to Switching and Automata Theory, McGraw-Hill, 1965.

[10]

U. Hinsberger and R. Kolla, "Boolean matching for large libraries," in Proc. IEEE/ACM Design Automation Conf., pp. 206--211, June 1998.

Digital Library

[11]

S. L. Hurst, D. M. Miller, and J. C. Muzio, Spectral Techniques in Digital Logic, Academic Press Inc., 1985.

Digital Library

[12]

M. Hütter and M. Scheppler, "Memory efficient and fast Boolean matching for large functions using rectangle representation," in IEEE/ACM Int. Workshop on Logic Synthesis, May 2003.

[13]

R. Kolla, "Personal communication," June 2003.

[14]

Y.-T. Lai, S. Sastry, and M. Pedram, "Boolean matching using binary decision diagrams with applications to logic synthesis and verification," in Proc. IEEE Int. Conf. on Computer Design, pp. 452--458, Oct. 1992.

Digital Library

[15]

C. Liem and M. Lefebvre, "Performance directed technology mapping using constructive matching," in IEEE/ACM Int. Workshop on Logic Synthesis, May 1991.

[16]

F. Mailhot and G. De Micheli, "Algorithms for technology mapping based on binary decision diagrams and on Boolean operations," IEEE Trans. Computer-Aided Design of Integrated Circuits and Systems, vol. 12, no. 5, pp. 599--620, May 1993.

Digital Library

[17]

Y. Matsunaga, "A new algorithm for Boolean matching utilizing structural information." IEICE Trans. Information and Systems, vol. E78-D, no. 3, pp. 219--223, Mar. 1995.

[18]

J. Mohnke and S. Malik, "Permutation and phase independent Boolean comparison," in Proc. IEEE European Conf. on Design Automation, pp. 86--92, Feb. 1993.

[19]

S. Muroga, Logic Design and Switching Theory, John Wiley & Sons, 1979.

Digital Library

[20]

U. Schlichtmann, F. Brglez, and M. Hermann, "Characterization of Boolean functions for rapid matching in EPGA technology mapping," in Proc. IEEE/ACM Design Automation Conf., pp. 374--379, June 1992.

Digital Library

[21]

U. Schlichtmann, F. Brglez, and P. Schneider, "Efficient Boolean matching based on unique variable ordering," in IEEE/ACM Int. Workshop on Logic Synthesis, pp. 3b:1-3b:13, May 1993.

[22]

E. Schubert and W. Rosenstiel, "Combined spectral techniques for Boolean matching," in Proc. ACM Int. Symposium on Field-Programmable Gate Arrays, pp. 38--43, Feb. 1996.

Digital Library

[23]

C. Tsai and M. Marek-Sadowska, "Boolean functions classification via fixed polarity Reed-Mueller forms," IEEE Trans. Comput., vol. 46, no. 2, pp. 173--186, Feb. 1997.

Digital Library

[24]

K.-H. Wang, T. Hwang, and C. Chen, "Exploiting communication complexity for Boolean matching," IEEE Trans. Computer-Aided Design of Integrated Circuits and Systems, vol. 15, no. 10, pp. 1249--1256, Oct. 1996.

Digital Library

[25]

Q. Wu, C. Y. R. Chen, and J. M. Acken, "Efficient Boolean matching algorithm for cell libraries," in Proc. IEEE Int. Conf. on Computer Design, pp. 36--39, Oct. 1994.

Digital Library

Cited By

Zhou XWang LMishchenko A(2019)Fast Adjustable NPN Classification Using Generalized SymmetriesACM Transactions on Reconfigurable Technology and Systems10.1145/331391712:2(1-16)Online publication date: 12-Apr-2019
https://dl.acm.org/doi/10.1145/3313917
Mishchenko ABrayton RChatterjee SNassif SRoychowdhury J(2008)Boolean factoring and decomposition of logic networksProceedings of the 2008 IEEE/ACM International Conference on Computer-Aided Design10.5555/1509456.1509477(38-44)Online publication date: 10-Nov-2008
https://dl.acm.org/doi/10.5555/1509456.1509477
Abdollahi AFix L(2008)Signature based Boolean matching in the presence of don't caresProceedings of the 45th annual Design Automation Conference10.1145/1391469.1391635(642-647)Online publication date: 8-Jun-2008
https://dl.acm.org/doi/10.1145/1391469.1391635
Show More Cited By

Recommendations

Efficient Computation of Canonical Form under Variable Permutation and Negation for Boolean Matching in Large Libraries

This paper presents an efficient technique for solving a Boolean matching problem in cell-library binding, where the number of cells in the library is large. As a basis of the Boolean matching, we use the notion NP-representative (NPR): two functions ...
A spectral method for Boolean function matching
EDTC '96: Proceedings of the 1996 European conference on Design and Test

An approach to Boolean matching with respect to NPN operations, i.e. negation of the function, permutation of the inputs and negation of the inputs, is presented. The method is based on a canonical form defined in the Hadamard spectral domain. When ...
An efficient cost-based canonical form for Boolean matching
GLSVLSI '07: Proceedings of the 17th ACM Great Lakes symposium on VLSI

In this paper, we present new canonical forms for P, NP and NPN equivalence relations on boolean functions. The canonical forms are based on the minimization of a cost function. With respect to previous approaches based on cost minimization, our ...

Comments

Information & Contributors

Information

Published In

cover image ACM Conferences

ASP-DAC '04: Proceedings of the 2004 Asia and South Pacific Design Automation Conference

January 2004

957 pages

ISBN:0780381750

General Chair:
Masaharu Imai
Osaka University

Sponsors

IPSJ: Information Processing Society of Japan
IEEE Circuits and Systems Society
SIGDA: ACM Special Interest Group on Design Automation
IEICE: Institute of Electronics, Information and Communication Engineers

Publisher

IEEE Press

Publication History

Published: 27 January 2004

Check for updates

Author Tags

Qualifiers

Article

Conference

ASPDAC04

Sponsor:

IPSJ
SIGDA
IEICE

ASPDAC04: Asia and South Pacific Design Automation Conference 2004

January 27 - 30, 2004

Yokohama, Japan

Acceptance Rates

Overall Acceptance Rate 466 of 1,454 submissions, 32%

Upcoming Conference

ASPDAC '25

Sponsor:
sigda

30th Asia and South Pacific Design Automation Conference

January 20 - 23, 2025

Tokyo , Japan

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

6
Total Citations
View Citations
224
Total Downloads

Downloads (Last 12 months)1
Downloads (Last 6 weeks)0

Reflects downloads up to 09 Nov 2024

Other Metrics

View Author Metrics

Citations

Cited By

Zhou XWang LMishchenko A(2019)Fast Adjustable NPN Classification Using Generalized SymmetriesACM Transactions on Reconfigurable Technology and Systems10.1145/331391712:2(1-16)Online publication date: 12-Apr-2019
https://dl.acm.org/doi/10.1145/3313917
Mishchenko ABrayton RChatterjee SNassif SRoychowdhury J(2008)Boolean factoring and decomposition of logic networksProceedings of the 2008 IEEE/ACM International Conference on Computer-Aided Design10.5555/1509456.1509477(38-44)Online publication date: 10-Nov-2008
https://dl.acm.org/doi/10.5555/1509456.1509477
Abdollahi AFix L(2008)Signature based Boolean matching in the presence of don't caresProceedings of the 45th annual Design Automation Conference10.1145/1391469.1391635(642-647)Online publication date: 8-Jun-2008
https://dl.acm.org/doi/10.1145/1391469.1391635
Agosta GBruschi FPelosi GSciuto DLevitan S(2007)A unified approach to canonical form-based Boolean matchingProceedings of the 44th annual Design Automation Conference10.1145/1278480.1278689(841-846)Online publication date: 4-Jun-2007
https://dl.acm.org/doi/10.1145/1278480.1278689
Chai DKuehlmann AGielen G(2006)Building a better Boolean matcher and symmetry detectorProceedings of the conference on Design, automation and test in Europe: Proceedings10.5555/1131481.1131780(1079-1084)Online publication date: 6-Mar-2006
https://dl.acm.org/doi/10.5555/1131481.1131780
Abdollahi APedram MJoyner WMartin GKahng A(2005)A new canonical form for fast boolean matching in logic synthesis and verificationProceedings of the 42nd annual Design Automation Conference10.1145/1065579.1065681(379-384)Online publication date: 13-Jun-2005
https://dl.acm.org/doi/10.1145/1065579.1065681

View Options

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 Publication

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

Media

Figures

Other

Tables

View Table of Contents