Size and energy of threshold circuits computing mod functions

Kei Uchizawa, Takao Nishizeki, Eiji Takimoto

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Citations (Scopus)

Abstract

Let C be a threshold logic circuit computing a Boolean function MOD m:{0,1}n → {0,1}, where n ≥1 and m≥2. Then C outputs "0" if the number of "1"s in an input x ∈ {0, 1} n to C is a multiple of m and, otherwise, C outputs "1." The function MOD2 is the so-called PARITY function, and MOD n+1 is the OR function. Let s be the size of the circuit C, that is, C consists of s threshold gates, and let e be the energy complexity of C, that is, at most e gates in C output "1" for any input x ∈{ 0, 1} n . In the paper, we prove that a very simple inequality n/(m-1)≤s e holds for every circuit C computing MOD m . The inequality implies that there is a tradeoff between the size s and energy complexity e of threshold circuits computing MOD m , and yields a lower bound e=Ω((logn-logm)/loglogn) on e if s=O(polylog(n)). We actually obtain a general result on the so-called generalized mod function, from which the result on the ordinary mod function MOD m immediately follows. Our results on threshold circuits can be extended to a more general class of circuits, called unate circuits.

Original languageEnglish
Title of host publicationMathematical Foundations of Computer Science 2009 - 34th International Symposium, MFCS 2009, Proceedings
Pages724-735
Number of pages12
DOIs
Publication statusPublished - Sep 28 2009
Event34th International Symposium on Mathematical Foundations of Computer Science 2009, MFCS 2009 - Novy Smokovec, High Tatras, Slovakia
Duration: Aug 24 2009Aug 28 2009

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5734 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other34th International Symposium on Mathematical Foundations of Computer Science 2009, MFCS 2009
CountrySlovakia
CityNovy Smokovec, High Tatras
Period8/24/098/28/09

All Science Journal Classification (ASJC) codes

  • Computer Science(all)
  • Theoretical Computer Science

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    Uchizawa, K., Nishizeki, T., & Takimoto, E. (2009). Size and energy of threshold circuits computing mod functions. In Mathematical Foundations of Computer Science 2009 - 34th International Symposium, MFCS 2009, Proceedings (pp. 724-735). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5734 LNCS). https://doi.org/10.1007/978-3-642-03816-7_61