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

Rafi Heiman, Ilan Newman, Avi Wigderson

Research output: Contribution to journalArticlepeer-review


TC0 is the class 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 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-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 towards proving TC0 ≠ NC1; generalizing our lower bound to all functions in TC0 would establish this separation. Another structural result we obtain is that a read-once threshold formula uniquely represents the function it computes.

Original languageEnglish
Pages (from-to)63-76
Number of pages14
JournalTheoretical Computer Science
Issue number1
StatePublished - 4 Jan 1993
Externally publishedYes

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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