 
Summary: LOWER BOUNDS FOR THRESHOLD AND SYMMETRIC FUNCTIONS
IN PARALLEL COMPUTATION
Yossi Azar \Lambda
Computer Science Department
Stanford University
Stanford, CA 943052140
Abstract
We consider the family of decision problems of the threshold languages L g . A threshold
language L g is the set of n bit vectors having at least g(n) ``1''s. Using a new technique for
controlling the size and structure of a hypergraph by a potential function, we prove lower bounds for
these decision problems on a PRIORITY PRAM with m shared memory cells and any polynomial
number of processors. The lower bounds are almost tight for the admissible range (m Ÿ n ffl ). By
combining our results with the results of Vishkin and Wigderson and the results of Li and Yesha we
are able to show a complexity gap between an m cell PRIORITY PRAM having an exponential (or
unlimited) number of processors and one having only a polynomial number. A consequence of our
results is that PRIORITY PRAM and ARBITRARY PRAM with m shared memory cells and any
given polynomial number of processors have the same power (up to a small factor) for computing
symmetric functions.
\Lambda Supported by a Weizmann Fellowship and by contract ONR N0001488K0166.
