# Arithmetic constant-depth circuit complexity classes

Chen, Hubie
(2003)
Arithmetic constant-depth circuit complexity classes.
In:
Rovan, B. and Vojtas, P. (eds.)
*28th International Symposium: Mathematical Foundations of Computer Science.*
Lecture Notes in Computer Science 2724.
Springer, pp. 328-337.
ISBN 9783540406716.

## Abstract

The boolean circuit complexity classes AC 0 ⊆ AC 0[m] ⊆ TC 0 ⊆ NC 1 have been studied intensely. Other than NC 1, they are defined by constant-depth circuits of polynomial size and unbounded fan-in over some set of allowed gates. One reason for interest in these classes is that they contain the boundary marking the limits of current lower bound technology: such technology exists for AC 0 and some of the classes AC 0[m], while the other classes AC 0[m] as well as TC 0 lack such technology. Continuing a line of research originating from Valiant’s work on the counting class \ensuremath♯P , the arithmetic circuit complexity classes \ensuremath♯AC0 and \ensuremath♯NC1 have recently been studied. In this paper, we define and investigate the classes \ensuremath♯AC0[m] and \ensuremath♯TC0 , new arithmetic circuit complexity classes that are defined by constant-depth circuits and are analogues of the classes AC 0[m] and TC 0.

## Metadata

Item Type: | Book Section |
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School: | Birkbeck Faculties and Schools > Faculty of Science > School of Computing and Mathematical Sciences |

Depositing User: | Sarah Hall |

Date Deposited: | 09 Mar 2021 17:18 |

Last Modified: | 09 Aug 2023 12:50 |

URI: | https://eprints.bbk.ac.uk/id/eprint/43359 |

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