On the Complexity of Boolean Functions in Different Characteristics

Every Boolean function on n variables can be expressed as a unique multivariate polynomial modulo p for every prime p. In this work, we study how the degree of a function in one characteristic affects its complexity in other characteristics. We establish the following general principle: functions with low degree modulo p must have high complexity in every other characteristic q. More precisely, we show the following results about Boolean functions f : {0, 1}n {0, 1} which depend on all n variables, and distinct primes p, q:

• Type: Conference
• Year: 2009
• Where: COCO
• Authors: Parikshit Gopalan, Shachar Lovett, Amir Shpilka
• Keywords: Algorithms, Boolean Function, COCO 2009, Modulo P, Modulo Q