On read-once threshold formulae and their randomized decision tree complexity

Rafi Heiman, Ilan Newman, Avi Wigderson

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

TC0 is the class of functions computable by polynomial-size, constant-depth formulae with threshold gates. Read-once TC0 (RO-TC0) is the subclass of TC0 which restricts every variable to exactly one occurrence in the formula. The main result is a (tight) linear lower bound on the randomized decision tree complexity of any function in RO-TC0. 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 toward proving TC0 ≠ NC1; generalizing the lower bound to all functions in TC0 will establish this separation. Another structural result is that a read-once threshold formula uniquely represents the function it computes.

Original languageEnglish
Title of host publicationProc Fifth Annu Struct Complexity Theor
PublisherPubl by IEEE
Pages78-87
Number of pages10
ISBN (Print)0818620722
StatePublished - 1990
Externally publishedYes
EventProceedings of the Fifth Annual Structure in Complexity Theory Conference - Barcelona, Spain
Duration: 8 Jul 199011 Jul 1990

Publication series

NameProc Fifth Annu Struct Complexity Theor

Conference

ConferenceProceedings of the Fifth Annual Structure in Complexity Theory Conference
CityBarcelona, Spain
Period8/07/9011/07/90

ASJC Scopus subject areas

  • Engineering (all)

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