### Abstract

In this paper, we consider a logic circuit (i.e., a combinatorial circuit consisting of gates, each of which computes a Boolean function) C computing a symmetric Boolean function f, and investigate a relationship between two complexity measures, energy e and fan-in l of C, where the energy e is the maximum number of gates outputting "1" over all inputs to C, and the fan-in l is the maximum number of inputs of every gate in C. We first prove that any symmetric Boolean function f of n variables can be computed by a logic circuit of energy e=O(n/l) and fan-in l, and then provide an almost tight lower bound e≥âŒ̂(n-^{mf})/lâŒ‰ where ^{mf} is the maximum numbers of consecutive "0"s or "1"s in the value vector of f. Our results imply that there exists a tradeoff between the energy and fan-in of logic circuits computing a symmetric Boolean function.

Original language | English |
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Pages (from-to) | 74-80 |

Number of pages | 7 |

Journal | Theoretical Computer Science |

Volume | 505 |

DOIs | |

Publication status | Published - 2013 Jan 4 |

### Keywords

- Boolean functions
- Energy complexity
- Fan-in
- MOD functions
- Parity function
- Symmetric functions
- Threshold circuits

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)