, Volume 24, Issue 3, pp 371–380 | Cite as

Depth-2 Threshold Circuits

Provable Limitations
  • Meena MahajanEmail author
General Article


Circuits with linear threshold functions as primitives are a natural model for computation in the brain. Small threshold circuits of depth two cannot compute most functions, but how do we prove such a statement? And how do we lay our hands on explicit functions that they cannot compute? This article gives an overview of the landscape.


Computation circuits threshold functions complexity neural networks perception 


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Suggested Reading

  1. [1]
    Eyal Kushilevitz and Noam Nisan, Communication Complexity, Cambridge University Press, 1997.Google Scholar
  2. [2]
    Mikael Goldmann, Johan Håastad and Alexander A Razborov, Majority Gates vs. General Weighted Threshold Gates, Computational Complexity, Vol.2, pp.277–300, 1992.CrossRefGoogle Scholar
  3. [3]
    Thomas Hofmeister, A Note on the Simulation of Exponential Threshold Weights, Computing and Combinatorics, Second Annual International Conference, COCOON’ 96, Hong Kong, June 17–19, 1996, Proceedings, pp.136–141, 1996.Google Scholar
  4. [4]
    András Hajnal, Wolfgang Maass, Pavel Pudlák, Mario Szegedy, and György Turán, Threshold Circuits of Bounded Depth, Journal of Computer and System Sciences, Vol.46, No.2, pp.129–154, 1993.CrossRefGoogle Scholar
  5. [5]
    Harry Buhrman, Nikolay Vereshchagin, and Ronald de Wolf, On Computation and Communication with Small Bias, Proceedings of the Twenty-Second Annual IEEE Conference on Computational Complexity, CCC’ 07, pp.24–32. IEEE Computer Society, 2007.Google Scholar
  6. [6]
    Jürgen Forster, Matthias Krause, Satyanarayana V Lokam, Rustam Mubarakzjanov, Niels Schmitt and Hans Ulrich Simon, Relations Between Communication Complexity, Linear Arrangements, and Computational Complexity, FST TCS 2001: Foundations of Software Technology and Theoretical Computer Science, 21st Conference, Bangalore, India, December 13–15, 2001, Proceedings, pp.171–182, 2001.Google Scholar
  7. [7]
    Arkadev Chattopadhyay and Nikhil S Mande, A Short List of Equalities Induces Large Sign Rank, Proc. 59th Annual IEEE Symposium on Foundations of Computer Science (FOCS), 2018. Preliminary version in ECCC TR 2017-083.Google Scholar
  8. [8]
    Jürgen Forster, A Linear Lower Bound on the Unbounded Error Probabilistic Communication Complexity, Journal of Computer and System Sciences, Vol.65, No.4, pp.612–625, 2002.CrossRefGoogle Scholar

Copyright information

© Indian Academy of Sciences 2019

Authors and Affiliations

  1. 1.The Institute of Mathematical Sciences (HBNI) CIT CampusChennaiIndia

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