### Abstract

In the paper we show that there is a close relationship between the energy complexity and the depth of threshold circuits computing any Boolean function although they have completely different physical meanings. Suppose that a Boolean function f can be computed by a threshold circuit C of energy complexity e and hence at most e threshold gates in C output "1" for any input to C. We then prove that the function f can be computed also by a threshold circuit C′ of depth 2e + 1 and hence the parallel computation time of C′ is 2e + 1. If the size of C is s, that is, there are s threshold gates in C, then the size s′ of C′ is s′ = 2es + 1. Thus, if the size s of C is polynomial in the number n of input variables, then the size s′ of C′ is polynomial in n, too.

Original language | English |
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Title of host publication | Fundamentals of Computation Theory - 17th International Symposium, FCT 2009, Proceedings |

Pages | 335-345 |

Number of pages | 11 |

DOIs | |

Publication status | Published - Nov 9 2009 |

Event | 17th International Symposium on Fundamentals of Computation Theory, FCT 2009 - Wroclaw, Poland Duration: Sep 2 2009 → Sep 4 2009 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 5699 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 17th International Symposium on Fundamentals of Computation Theory, FCT 2009 |
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Country | Poland |

City | Wroclaw |

Period | 9/2/09 → 9/4/09 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Fundamentals of Computation Theory - 17th International Symposium, FCT 2009, Proceedings*(pp. 335-345). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5699 LNCS). https://doi.org/10.1007/978-3-642-03409-1_30