@inproceedings{23793e9f22834650a7037ea48237bd3b,

title = "On read-once threshold formulae and their randomized decision tree complexity",

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.",

author = "Rafi Heiman and Ilan Newman and Avi Wigderson",

year = "1990",

language = "English",

isbn = "0818620722",

series = "Proc Fifth Annu Struct Complexity Theor",

publisher = "Publ by IEEE",

pages = "78--87",

booktitle = "Proc Fifth Annu Struct Complexity Theor",

note = "Proceedings of the Fifth Annual Structure in Complexity Theory Conference ; Conference date: 08-07-1990 Through 11-07-1990",

}