## Abstract

TC^{0} is the class functions computable by polynomial-size, constant-depth formulae with threshold gates. Read-once TC^{0} (RO-TC^{0}) is the subclass of TC^{0} which restricts every variable to occur exactly once in the formula. Our main result is a (tight) linear lower bound on the randomized decision tree complexity of any function in RO-TC^{0}. This relationship between threshold circuits and decision trees bears significance on both models of computation. Regarding decision trees, this is the first class of functions for which such a strong bound is known. Regarding threshold circuits, it may be considered as a possible first step towards proving TC^{0} ≠ NC^{1}; generalizing our lower bound to all functions in TC^{0} would establish this separation. Another structural result we obtain is that a read-once threshold formula uniquely represents the function it computes.

Original language | English |
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Pages (from-to) | 63-76 |

Number of pages | 14 |

Journal | Theoretical Computer Science |

Volume | 107 |

Issue number | 1 |

DOIs | |

State | Published - 4 Jan 1993 |

Externally published | Yes |

## ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science (all)