Representing Boolean functions as polynomials modulo composite numbers
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
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RAZBOROV [RA86] HAS RECENTLY PROVED THAT A CONSTANT DEPTH UNBOUNDED FAN- IN CIRCUIT WITH `AND'' AND `PARITY'' GATES REQUIRES EXPONENTIAL SIZE TO COMPUTE THE MAJORITY FUNCTION, AFFIRMING A FIVE YEAR OLD CONJECTURE [FSS81]. HERE WE EXTEND HIS TECHNIQUE TO SHOW THE SAME RESULT FOR CIRCUITS WITH `AND'' GATES AND `MOD-P'' GATES FOR PRIME P, WHERE A MOD-P GATE OUTPUTS ONE IF THE SUM MOD P OF ITS (BOOLEAN) INPUTS IS NONZERO AND ZERO OTHERWISE.