Title :
A lower bound for primality
Author :
Allender, Eric ; Saks, Michael ; Shparlinski, Igor
Author_Institution :
Dept. of Comput. Sci., Rutgers Univ., Piscataway, NJ, USA
Abstract :
Recent work by Bernasconi, Damm and Shparlinski proved lower bounds on the circuit complexity of the square-free numbers, and raised as an open question if similar (or stronger) lower bounds could be proved for the set of prime numbers. In this short note, we answer this question affirmatively, by showing that the set of prime numbers (represented in the usual binary notation) is not contained in AC0 [p] for any prime p. Similar lower bounds are presented for the set of square-free numbers, and for the problem of computing the greatest common divisor of two numbers
Keywords :
circuit complexity; computational complexity; circuit complexity; greatest common divisor; lower bound; primality; square-free numbers; Circuit testing; Computer science; Encoding; Mathematics; Physics computing; Polynomials; Upper bound;
Conference_Titel :
Computational Complexity, 1999. Proceedings. Fourteenth Annual IEEE Conference on
Conference_Location :
Atlanta, GA
Print_ISBN :
0-7695-0075-7
DOI :
10.1109/CCC.1999.766257
