research-article

A Constructive Approach for Threshold Function Identification

Authors:

Yung-Chih Chen,

Chun-Yao WangAuthors Info & Claims

ACM Transactions on Design Automation of Electronic Systems, Volume 28, Issue 5

Article No.: 86, Pages 1 - 19

https://doi.org/10.1145/3606371

Published: 09 September 2023 Publication History

Abstract

Threshold Function (TF) is a subset of Boolean function that can be represented with a single linear threshold gate (LTG). In the research about threshold logic, the identification of TF is an important task that determines whether a given function is a TF or not. In this article, we propose a sufficient and necessary condition for a function being a TF. With the proposed sufficient and necessary condition, we devise a TF identification algorithm. The experimental results show that the proposed approach saves 80% CPU time for identifying all the 8-input NP-class TFs as compared with the state-of-the-art. Furthermore, the LTGs corresponding to the identified TFs obtained by the proposed approach have smaller weights and threshold values than the state-of-the-art.

References

[1]

Gurobi. https://www.gurobi.com/.

[2]

M. J. Avedillo, J. M. Quintana, H. Pettenghi, P. M. Kelly, and C. J. Thompson. 2003. Multi-threshold threshold logic circuit design using resonant tunnelling devices. Electron. Lett. 39, 21 (2003), 1.

[3]

Yung-Chih Chen, Hao-Ju Chang, and Li-Cheng Zheng. 2020. Don’t-care-based node minimization for threshold logic networks. In 57th ACM/IEEE Design Automation Conference (DAC’20). IEEE, 1–6.

[4]

Calvin C. Elgot. 1961. Truth functions realizable by single threshold organs. In 2nd Annual Symposium on Switching Circuit Theory and Logical Design (SWCT’61). IEEE, 225–245.

[5]

Sukumar Ghosh, Subir Bandyopadhyay, Sanjit Kumar Mitra, and Arun Kumar Choudhury. 1972. Simple methods for the testing of 2-summability of Boolean functions and isobaricity of threshold functions. IEEE Trans. Comput. 100, 5 (1972), 503–507.

Digital Library

[6]

David Goldhaber-Gordon, Michael S. Montemerlo, J. Christopher Love, Gregory J. Opiteck, and James C. Ellenbogen. 1997. Overview of nanoelectronic devices. Proc. IEEE 85, 4 (1997), 521–540.

[7]

Wen-Chih Hsu, Chia-Chun Lin, Yi-Ting Li, Yung-Chih Chen, and Chun-Yao Wang. 2021. On reduction of computations for threshold function identification. In IEEE 34th International System-on-Chip Conference (SOCC’21). IEEE, 146–151.

[8]

Pin-Yi Kuo, Chun-Yao Wang, and Ching-Yi Huang. 2011. On rewiring and simplification for canonicity in threshold logic circuits. In IEEE/ACM International Conference on Computer-Aided Design (ICCAD’11). IEEE, 396–403.

Digital Library

[9]

Siang-Yun Lee, Nian-Ze Lee, and Jie-Hong R. Jiang. 2018. Canonicalization of threshold logic representation and its applications. In IEEE/ACM International Conference on Computer-Aided Design (ICCAD’18). IEEE, 1–8.

Digital Library

[10]

Siang-Yun Lee, Nian-Ze Lee, and Jie-Hong R. Jiang. 2019. Searching parallel separating hyperplanes for effective compression of threshold logic networks. In IEEE/ACM International Conference on Computer-Aided Design (ICCAD’19). IEEE, 1–8.

[11]

Chia-Chun Lin, Chiao-Wei Huang, Chun-Yao Wang, and Yung-Chih Chen. 2017. In&Out: Restructuring for threshold logic network optimization. In 18th International Symposium on Quality Electronic Design (ISQED’17). IEEE, 413–418.

[12]

Chia-Chun Lin, Ciao-Syun Lin, You-Hsuen Tsai, Yung-Chih Chen, and Chun-Yao Wang. 2021. Don’t care computation and De Morgan transformation for threshold logic network optimization. IEEE Trans. Comput.-Aid. Des. Integ. Circ. Syst. 41, 5 (2021), 1412–1422.

[13]

Chia-Chun Lin, Chin-Heng Liu, Yung-Chih Chen, and Chun-Yao Wang. 2020. A new necessary condition for threshold function identification. IEEE Trans. Comput.-Aid. Des. Integ. Circ. Syst. 39, 12 (2020), 5304–5308.

[14]

Chia-Chun Lin, Chun-Yao Wang, Yung-Chih Chen, and Ching-Yi Huang. 2014. Rewiring for threshold logic circuit minimization. In Design, Automation & Test in Europe Conference & Exhibition (DATE’14). IEEE, 1–6.

[15]

Chin-Heng Liu, Chia-Chun Lin, Yung-Chih Chen, Chia-Cheng Wu, Chun-Yao Wang, and Shigeru Yamashita. 2018. Threshold function identification by redundancy removal and comprehensive weight assignments. IEEE Trans. Comput.-Aid. Des. Integ. Circ. Syst. 38, 12 (2018), 2284–2297.

Digital Library

[16]

Vassilios A. Mardiris, Georgios Ch. Sirakoulis, and Ioannis G. Karafyllidis. 2014. Automated design architecture for 1-D cellular automata using quantum cellular automata. IEEE Trans. Comput. 64, 9 (2014), 2476–2489.

Digital Library

[17]

Saburo Muroga. 1971. Threshold Logic and Its Applications. Wiley, New York, NY.

[18]

Saburo Muroga, I. Toda, and M. Kondo. 1962. Majority decision functions of up to six variables. Math. Comput. 16, 80 (1962), 459–472.

[19]

Saburo Muroga, Teiichi Tsuboi, and Charles Richmond Baugh. 1970. Enumeration of threshold functions of eight variables. IEEE Trans. Comput. 100, 9 (1970), 818–825.

Digital Library

[20]

Augusto Neutzling, Mayler G. A. Martins, Vinicius Callegaro, Andre I. Reis, and Renato P. Ribas. 2017. A simple and effective heuristic method for threshold logic identification. IEEE Trans. Comput.-Aid. Des. Integ. Circ. Syst. 37, 5 (2017), 1023–1036.

[21]

Georgios Papandroulidakis, Alexander Serb, Ali Khiat, Geoff V. Merrett, and Themis Prodromakis. 2019. Practical implementation of memristor-based threshold logic gates. IEEE Trans. Circ. Syst. I: Reg. Pap. 66, 8 (2019), 3041–3051.

[22]

Vinay Saripalli, Lu Liu, Suman Datta, and Vijaykrishnan Narayanan. 2010. Energy-delay performance of nanoscale transistors exhibiting single electron behavior and associated logic circuits. J. Low Power Electron. 6, 3 (2010), 415–428.

[23]

Anil K. Sarje and Nripendra N. Biswas. 1979. A new approach to 2-asummability testing. IEEE Trans. Comput. 28, 10 (1979), 798–801.

Digital Library

[24]

Chen-Kuan Tsai, Chun-Yao Wang, Ching-Yi Huang, and Yung-Chih Chen. 2013. Sensitization criterion for threshold logic circuits and its application. In IEEE/ACM International Conference on Computer-Aided Design (ICCAD’13). IEEE, 226–233.

[25]

Robert O. Winder. 1961. Single stage threshold logic. In 2nd Annual Symposium on Switching Circuit Theory and Logical Design (SWCT’61). IEEE, 321–332.

[26]

Rui Zhang, Pallav Gupta, Lin Zhong, and Niraj K. Jha. 2004. Threshold network synthesis and optimization and its application to nanotechnologies. IEEE Trans. Comput.-Aid. Des. Integ. Circ. Syst. 24, 1 (2004), 107–118.

Cited By

Yen CLi MLi YChen YChen IWang C(2024)9-Input Threshold Function Identification Using a New Necessary Condition of Threshold FunctionIEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems10.1109/TCAD.2024.339966443:12(4676-4686)Online publication date: Dec-2024
https://doi.org/10.1109/TCAD.2024.3399664

Index Terms

A Constructive Approach for Threshold Function Identification
1. Theory of computation
  1. Design and analysis of algorithms

Recommendations

MultiFunction Threshold Gates

Threshold logic gates, up to now, generally have been presumed to provide a single function of the input variables. The threshold gates that have been integrated [1]-4] were naturally double-sided and provided complementary outputs or, more specifically,...
Variable-Threshold Threshold Elements

Abstract Variable-threshold threshold elements (V-T threshold elements) are threshold elements in which the weights are fixed while the threshold may be varied. When the threshold is varied, a set of functions is generated.
Efficient Threshold Architectures with Bounded Fan-Ins for Exclusive-ORs
SIPS '12: Proceedings of the 2012 IEEE Workshop on Signal Processing Systems

As process technologies scale into nanometer region, new opportunities as well as challenges arise. Some emerging nanotechnology devices that are promising candidates to replace the CMOS technology are particularly suitable for threshold logic ...

Comments

Information & Contributors

Information

Published In

cover image ACM Transactions on Design Automation of Electronic Systems

ACM Transactions on Design Automation of Electronic Systems Volume 28, Issue 5

September 2023

475 pages

ISSN:1084-4309

EISSN:1557-7309

DOI:10.1145/3623508

Editor:
X. Sharon Hu
University of Notre Dame, USA

Issue’s Table of Contents

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 the author(s) 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].

Publisher

Association for Computing Machinery

New York, NY, United States

Journal Family

ACM Journals for the Design of Smart and Connected Systems

Publication History

Published: 09 September 2023

Online AM: 30 June 2023

Accepted: 08 June 2023

Revised: 24 May 2023

Received: 29 November 2022

Published in TODAES Volume 28, Issue 5

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Author Tags

Qualifiers

Research-article

Funding Sources

National Science and Technology Council (Taiwan)

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

1
Total Citations
View Citations
116
Total Downloads

Downloads (Last 12 months)43
Downloads (Last 6 weeks)4

Reflects downloads up to 14 Jan 2025

Other Metrics

View Author Metrics

Citations

Cited By

Yen CLi MLi YChen YChen IWang C(2024)9-Input Threshold Function Identification Using a New Necessary Condition of Threshold FunctionIEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems10.1109/TCAD.2024.339966443:12(4676-4686)Online publication date: Dec-2024
https://doi.org/10.1109/TCAD.2024.3399664

View Options

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

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

Full Text

View this article in Full Text.

Media

Figures

Other

Tables

View full text|Download PDF

View Issue’s Table of Contents