## Abstract

The energy of a threshold circuit C is defined to be the maximum number of gates outputting ones for an input assignment, where the maximum is taken over all the input assignments. In this paper, we study computational power of threshold circuits of energy at most two. We present several results showing that the computational power of threshold circuits of energy one and the counterpart of energy two are remarkably different. In particular, we give an explicit function which requires an exponential size for threshold circuits of energy one, but is computable by a threshold circuit of size just two and energy two. We also consider MOD functions and Generalized Inner Product functions, and show that these functions also require exponential size for threshold circuits of energy one, but are computable by threshold circuits of substantially less size and energy two.

Original language | English |
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Pages (from-to) | 1431-1439 |

Number of pages | 9 |

Journal | IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences |

Volume | E101A |

Issue number | 9 |

DOIs | |

Publication status | Published - 2018 Sep |

Externally published | Yes |

## Keywords

- Circuit complexity
- Energy complexity
- MOD function
- Neural network
- Threshold circuit

## ASJC Scopus subject areas

- Signal Processing
- Computer Graphics and Computer-Aided Design
- Electrical and Electronic Engineering
- Applied Mathematics