In this paper, we consider a biologically-inspired Boolean function Pn D that models a simple task of detecting global spatial patterns on a two- dimensional map. We prove that Pn D is computable by a threshold circuit of size (i.e., number of gates) O(√n log n), which is an improvement on the previous upper bound O(n), while our circuit has larger depth O(√n) and total wire length O(n log2 n). Moreover, we demonstrate that the size of our circuit is nearly optimal up to a logarithmic factor: we show that any threshold circuit computing Pn D has size Ω (√ n= log n).
ASJC Scopus subject areas
- Theoretical Computer Science
- Computer Science(all)
- Computer Science Applications
- Geometry and Topology
- Computational Theory and Mathematics