Threshold circuits for global patterns in 2-dimensional maps

Kei Uchizawa; Daiki Yashima; Xiao Zhou

doi:10.1007/978-3-319-15612-5_27

Threshold circuits for global patterns in 2-dimensional maps

Kei Uchizawa, Daiki Yashima, Xiao Zhou

INF - System Information Sciences

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

1 Citation (Scopus)

Abstract

In this paper, we consider a biologically-inspired Boolean function, called Pⁿ _D, which models a task for detecting specific global spatial arrangements of local visual patterns on a 2-dimensional map. We prove that Pⁿ _D is computable by a threshold circuit of size O(√ n log n), which is improvement on the previous upper bound O(n). We also show that the size of our circuit is almost optimal up to logarithmic factor: we show that any threshold circuit computing Pⁿ _D needs size Ω(√ n/ log n).

Original language	English
Title of host publication	WALCOM
Subtitle of host publication	Algorithms and Computation - 9th InternationalWorkshop,WALCOM 2015, Proceedings
Editors	M. Sohel Rahman, Etsuji Tomita
Publisher	Springer Verlag
Pages	306-316
Number of pages	11
ISBN (Electronic)	9783319156118
DOIs	https://doi.org/10.1007/978-3-319-15612-5_27
Publication status	Published - 2015
Event	9th International Workshop on Algorithms and Computation, WALCOM 2015 - Dhaka, Bangladesh Duration: 2015 Feb 26 → 2015 Feb 28

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	8973
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	9th International Workshop on Algorithms and Computation, WALCOM 2015
Country/Territory	Bangladesh
City	Dhaka
Period	15/2/26 → 15/2/28

ASJC Scopus subject areas

Theoretical Computer Science
Computer Science(all)

Access to Document

10.1007/978-3-319-15612-5_27

Cite this

Uchizawa, K., Yashima, D., & Zhou, X. (2015). Threshold circuits for global patterns in 2-dimensional maps. In M. S. Rahman, & E. Tomita (Eds.), WALCOM: Algorithms and Computation - 9th InternationalWorkshop,WALCOM 2015, Proceedings (pp. 306-316). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8973). Springer Verlag. https://doi.org/10.1007/978-3-319-15612-5_27

Threshold circuits for global patterns in 2-dimensional maps. / Uchizawa, Kei; Yashima, Daiki; Zhou, Xiao.

WALCOM: Algorithms and Computation - 9th InternationalWorkshop,WALCOM 2015, Proceedings. ed. / M. Sohel Rahman; Etsuji Tomita. Springer Verlag, 2015. p. 306-316 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8973).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Uchizawa, K, Yashima, D & Zhou, X 2015, Threshold circuits for global patterns in 2-dimensional maps. in MS Rahman & E Tomita (eds), WALCOM: Algorithms and Computation - 9th InternationalWorkshop,WALCOM 2015, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 8973, Springer Verlag, pp. 306-316, 9th International Workshop on Algorithms and Computation, WALCOM 2015, Dhaka, Bangladesh, 15/2/26. https://doi.org/10.1007/978-3-319-15612-5_27

Uchizawa K, Yashima D, Zhou X. Threshold circuits for global patterns in 2-dimensional maps. In Rahman MS, Tomita E, editors, WALCOM: Algorithms and Computation - 9th InternationalWorkshop,WALCOM 2015, Proceedings. Springer Verlag. 2015. p. 306-316. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-319-15612-5_27

Uchizawa, Kei ; Yashima, Daiki ; Zhou, Xiao. / Threshold circuits for global patterns in 2-dimensional maps. WALCOM: Algorithms and Computation - 9th InternationalWorkshop,WALCOM 2015, Proceedings. editor / M. Sohel Rahman ; Etsuji Tomita. Springer Verlag, 2015. pp. 306-316 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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AB - In this paper, we consider a biologically-inspired Boolean function, called Pn D, which models a task for detecting specific global spatial arrangements of local visual patterns on a 2-dimensional map. We prove that Pn D is computable by a threshold circuit of size O(√ n log n), which is improvement on the previous upper bound O(n). We also show that the size of our circuit is almost optimal up to logarithmic factor: we show that any threshold circuit computing Pn D needs size Ω(√ n/ log n).

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Threshold circuits for global patterns in 2-dimensional maps

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