Learning Read-Constant Polynomials of Constant Degree Modulo Composites
Boolean functions that have constant degree polynomial rep- resentation over a xed nite ring form a natural and strict subclass of the complexity class ACC0. They are also precisely the functions com- putable efficiently by programs over xed and nite nilpotent groups. This class is not known to be learnable in any reasonable learning model. In this paper, we provide a deterministic polynomial time algorithm for learning Boolean functions represented by polynomials of constant degree over arbitrary nite rings from membership queries, with the additional constraint that each variable in the target polynomial appears in a con- stant number of monomials. Our algorithm extends to superconstant but low degree polynomials and still runs in quasipolynomial time.