TY - GEN
T1 - Threshold circuits for global patterns in 2-dimensional maps
AU - Uchizawa, Kei
AU - Yashima, Daiki
AU - Zhou, Xiao
N1 - Publisher Copyright:
© Springer International Publishing Switzerland 2015.
PY - 2015
Y1 - 2015
N2 - 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).
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).
UR - http://www.scopus.com/inward/record.url?scp=84923674085&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84923674085&partnerID=8YFLogxK
U2 - 10.1007/978-3-319-15612-5_27
DO - 10.1007/978-3-319-15612-5_27
M3 - Conference contribution
AN - SCOPUS:84923674085
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 306
EP - 316
BT - WALCOM
A2 - Rahman, M. Sohel
A2 - Tomita, Etsuji
PB - Springer Verlag
T2 - 9th International Workshop on Algorithms and Computation, WALCOM 2015
Y2 - 26 February 2015 through 28 February 2015
ER -