research-article

Fast Adjustable NPN Classification Using Generalized Symmetries

Authors:

Alan MishchenkoAuthors Info & Claims

ACM Transactions on Reconfigurable Technology and Systems (TRETS), Volume 12, Issue 2

Article No.: 7, Pages 1 - 16

https://doi.org/10.1145/3313917

Published: 12 April 2019 Publication History

Abstract

NPN classification of Boolean functions is a powerful technique used in many logic synthesis and technology mapping tools in both standard cell and FPGA design flows. Computing the canonical form is the most common approach of Boolean function classification. This article proposes two different hybrid NPN canonical forms and a new algorithm to compute them. By exploiting symmetries under different phase assignment as well as higher-order symmetries, the search space of NPN canonical form computation is pruned and the runtime is dramatically reduced. Nevertheless, the runtime for some difficult functions remains high. Fast heuristic method can be used for such functions to compute semi-canonical forms in a reasonable time. The proposed algorithm can be adjusted to be a slow exact algorithm or a fast heuristic algorithm with lower quality. For exact NPN classification, the proposed algorithm is 40× faster than state-of-the-art. For heuristic classification, the proposed algorithm has similar performance as state-of-the-art with a possibility to trade runtime for quality.

References

[1]

A. Kennings, A. Mishchenko, K. Vorwerk, V. Pevzner, and A. Kundu. 2010. Efficient FPGA resynthesis using precomputed LUT structures. In Proceedings of the International Conference on Field Programmable Logic and Applications (FPL’10). 532--537.

Digital Library

[2]

W. Yang, L. Wang, and A. Mishchenko. 2012. Lazy man's logic synthesis. In Proceedings of the International Conference on Computer-Aided Design (ICCAD’12). 597--604.

Digital Library

[3]

M. Soeken, L. G. Amarù, P. Gaillardon, and G. De Micheli. 2016. Optimizing majority-inverter graphs with functional hashing. In Proceedings of the Design, Automation 8 Test in Europe Conference 8 Exhibition (DATE’16).

Digital Library

[4]

A. Kennings, A. Mishchenko, K. Vorwerk, V. Pevzner, and A. Kundu. 2010. Generating efficient libraries for use in FPGA resynthesis algorithms. In Proceedings of the International Workshop on Logic and Synthesis (IWLS’10). 147--154.

[5]

S. Chatterjee, A. Mishchenko, R. K. Brayton, X. Wang, and T. Kam. 2006. Reducing structural bias in technology mapping. IEEE Trans. Comput.-Aided Design Integr. Circuits Syst. 25, 12 (2006), 2894--903.

Digital Library

[6]

A. Mishchenko, S. Cho, S. Chatterjee, and R. Brayton. 2007. Combinational and sequential mapping with priority cuts. In Proceedings of the International Conference on Computer-Aided Design (ICCAD’07). 354--361.

Digital Library

[7]

A. Mishchenko, R. Brayton, W. Feng, and J. W. Greene. 2015. Technology mapping into general programmable cells. In Proceedings of the ACM/SIGDA International Symposium on Field-Programmable Gate Arrays (FPGA’15). 70--73.

Digital Library

[8]

S. Ray, A. Mishchenko, N. Een, R. Brayton, S. Jang, and C. Chen. 2012. Mapping into LUT structures. In Proceedings of the Design, Automation 8 Test in Europe Conference 8 Exhibition (DATE’12). 1579--1584.

Digital Library

[9]

W. Feng, J. W. Greene, and A. Mishchenko. 2018. Improving FPGA performance with a S44 LUT structure. In Proceedings of the ACM/SIGDA International Symposium on Field-Programmable Gate Arrays (FPGA’18). 61--66.

Digital Library

[10]

U. Hinsberger and R. Kolla. 1998. Boolean matching for large libraries. In Proceedings of the Design Automation Conference (DAC’98), 206--211.

Digital Library

[11]

D. Chai and A. Kuehlmann. 2016. Building a better Boolean matcher and symmetry detector. In Proceedings of the Design, Automation 8 Test in Europe Conference 8 Exhibition (DATE’16). 1079--1084.

Digital Library

[12]

S. W. Golomb. 1959. On the classification of Boolean functions. IRE Trans. Circuit Theory CT-6 (1959), 176--186.

[13]

A. Abdollahi and M. Pedram. 2008. Symmetry detection and Boolean matching utilizing a signature-based canonical form of Boolean functions. IEEE Trans. Comput.-Aided Design Integr. Circuits Syst. 27, 6 (2008), 1128--1137.

Digital Library

[14]

G. Agosta, F. Bruschi, G. Pelosi, and D. Sciuto. 2009. A transform-parametric approach to Boolean matching. IEEE Trans. Comput.-Aided Design Integr. Circuits Syst. 28, 6 (2009), 805--817.

Digital Library

[15]

Z. Huang, L. Wang, Y. Nasikovskiy, and A. Mishchenko. 2013. Fast Boolean matching based on NPN classification. In Proceedings of the International Conference on Field Programmable Technology (ICFPT’13). 310--313.

[16]

C. C. Tsai, M. Marek-Sadowska, and D. Gatlin. 1997. Boolean function classification via fixed polarity Reed-Muller forms. IEEE Trans. Comput. 46, 2 (1997), 173--186.

Digital Library

[17]

A. Petkovska, M. Soeken, G. De Micheli, P. Ienne, and A. Mishchenko. 2016. Fast hierarchical NPN classification. In Proceedings of the International Conference on Field Programmable Logic and Applications (FPL’16), 61--64.

[18]

X. Zhou, L. Wang, P. Zhao, and A. Mishchenko. 2018. Fast adjustable NPN classification using generalized symmetries. In Proceedings of the International Conference on Field Programmable Logic and Applications (FPL’18). 1--7.

[19]

D. Slepian. 1952. On the number of symmetry types of Boolean functions of n variables. Can. J. Math. (1952), 185--193.

[20]

L. Benini and G. De Micheli. 1997. A survey of Boolean matching techniques for library binding. ACM Trans. Des. Autom. Electron. Syst. 2, 3 (1997), 193--226.

Digital Library

[21]

U. Hinsberger and R. Kolla. 1998. Boolean matching for large libraries. In Proceedings of the Design Automation Conference (DAC’98). 206--211.

Digital Library

[22]

D. Debnath and T. Sasao. 2004. Efficient computation of canonical form for Boolean matching in large libraries. In Proceedings of the Asia and South Pacific Design Automation Conference (ASP-DAC’04). 591--596.

Digital Library

[23]

E. Mailhot and G. De Micheli. 1993. Algorithms for technology mapping based on binary decision diagrams and on Boolean operations. IEEE Trans. Comput.-Aided Design Integr. Circuits Syst. 12, 5 (1993), 599--620.

Digital Library

[24]

E. M. Clarke, K. L. McMillan, X. Zhao, M. Fujita, and J. Yang. 1993. Spectral transforms for large Boolean functions with applications to technology mapping. In Proceedings of the Design Automation Conference (DAC’93), 54--60.

Digital Library

[25]

J. Rice. 2009. The autocorrelation transform and its application to the classification of Boolean functions. In Proceedings of the IEEE Pacific Rim Conference on Communications Computers and Signal Processing (PacRim’09). 94--99.

[26]

K. Wang, C. Chan, and J. Liu. 2009. Simulation and SAT-based Boolean matching for large Boolean networks. In Proceedings of the Design Automation Conference (DAC’09). 396--401.

Digital Library

[27]

C.-F. Lai, J.-H. R. Jiang, and K.-H. Wang. 2010. BooM: A decision procedure for Boolean matching with abstraction and dynamic learning. In Proceedings of the Design Automation Conference (DAC’10). 499--504.

Digital Library

[28]

M. Soeken, A. Mishchenko, A. Petkovska, B. Sterin, P. Ienne, R. Brayton, and G. De Micheli. 2016. Heuristic NPN classification for large functions using AIGs and LEXSAT. In Proceedings of the International Conference on Theory and Applications of Satisfiability Testing (SAT’16). 212--227.

[29]

C. C. Tsai and M. Marek-Sadowaska. 1996. Generalized Reed-Muller forms as a tool to detect symmetries. IEEE Trans. Comput. 45, 1 (1996), 33--40.

Digital Library

[30]

N. Kettle and A. King. 2006. An anytime symmetry detection algorithm for ROBDDs. In Proceedings of the Asia and South Pacific Design Automation Conference (ASP-DAC’06), 24--27.

[31]

V. N. Kravets and K. A. Sakallah. 2000. Generalized symmetries in Boolean functions. In Proceedings of the International Conference on Computer Aided Design (ICCAD’00). 526--532.

Digital Library

[32]

J. Ciric and C. Sechen. 2003. Efficient canonical form for Boolean matching of complex functions in large libraries. IEEE Trans. Comput.-Aided Design Integr. Circuits Syst. 22, 5 (2003), 535--544.

Digital Library

[33]

Q. Wu, C. Y. R. Chen, and J. M. Acken. 1994. Efficient Boolean matching algorithm for cell libraries. In Proceedings of the International Conference on Computer Design. 36--39.

Digital Library

[34]

Selmer M. Johnson. 1963. Generation of permutations by adjacent transposition. Math. Comp. 17 (1963), 282--285.

[35]

Berkeley Logic Synthesis and Verification Group. ABC: A System for Sequential Synthesis and Verification. Retrieved from http://www-cad.eecs. berkeley.edu/∼alanmi/abc.

[36]

R. Ashenhurst. 1957. The decomposition of switching functions. In Proceedings of the International Symposium on the Theory of Switching. Cambridge, Mass, 74--116.

Cited By

Zhang JZheng SNi LLi HLuo G(2023)Rethinking NPN Classification from Face and Point Characteristics of Boolean Functions2023 Design, Automation & Test in Europe Conference & Exhibition (DATE)10.23919/DATE56975.2023.10136889(1-6)Online publication date: Apr-2023
https://doi.org/10.23919/DATE56975.2023.10136889
Zhang YNi LZhang JLuo GLi HZheng S(2023)Fast Exact NPN Classification with Influence-Aided Canonical Form2023 IEEE/ACM International Conference on Computer Aided Design (ICCAD)10.1109/ICCAD57390.2023.10323783(01-09)Online publication date: 28-Oct-2023
https://doi.org/10.1109/ICCAD57390.2023.10323783
Zhu XTang RChen LLi XHuang XYuan MSheng WXu J(2023)A Database Dependent Framework for K-Input Maximum Fanout-Free Window Rewriting2023 60th ACM/IEEE Design Automation Conference (DAC)10.1109/DAC56929.2023.10247727(1-6)Online publication date: 9-Jul-2023
https://doi.org/10.1109/DAC56929.2023.10247727
Show More Cited By

Index Terms

Fast Adjustable NPN Classification Using Generalized Symmetries
1. Computer systems organization
  1. Architectures
    1. Other architectures
      1. Reconfigurable computing
2. Hardware
  1. Electronic design automation
    1. Logic synthesis

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Published In

cover image ACM Transactions on Reconfigurable Technology and Systems

ACM Transactions on Reconfigurable Technology and Systems Volume 12, Issue 2

June 2019

117 pages

ISSN:1936-7406

EISSN:1936-7414

DOI:10.1145/3322884

Editor:
Deming Chen
University of Illinois, Urbana-Champaign Urbana

Issue’s Table of Contents

Copyright © 2019 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

New York, NY, United States

Publication History

Published: 12 April 2019

Accepted: 01 February 2019

Received: 01 December 2018

Published in TRETS Volume 12, Issue 2

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Cited By

Zhang JZheng SNi LLi HLuo G(2023)Rethinking NPN Classification from Face and Point Characteristics of Boolean Functions2023 Design, Automation & Test in Europe Conference & Exhibition (DATE)10.23919/DATE56975.2023.10136889(1-6)Online publication date: Apr-2023
https://doi.org/10.23919/DATE56975.2023.10136889
Zhang YNi LZhang JLuo GLi HZheng S(2023)Fast Exact NPN Classification with Influence-Aided Canonical Form2023 IEEE/ACM International Conference on Computer Aided Design (ICCAD)10.1109/ICCAD57390.2023.10323783(01-09)Online publication date: 28-Oct-2023
https://doi.org/10.1109/ICCAD57390.2023.10323783
Zhu XTang RChen LLi XHuang XYuan MSheng WXu J(2023)A Database Dependent Framework for K-Input Maximum Fanout-Free Window Rewriting2023 60th ACM/IEEE Design Automation Conference (DAC)10.1109/DAC56929.2023.10247727(1-6)Online publication date: 9-Jul-2023
https://doi.org/10.1109/DAC56929.2023.10247727
Zhou XWang LMishchenko A(2020)Fast Exact NPN Classification by Co-Designing Canonical Form and Its Computation AlgorithmIEEE Transactions on Computers10.1109/TC.2020.297146669:9(1293-1307)Online publication date: 1-Sep-2020
https://doi.org/10.1109/TC.2020.2971466

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