PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Learning Read-Constant Polynomials of Constant Degree Modulo Composites
Arkadev Chattopadhyay, Ricard Gavaldà, Kristoffer Arnsfelt Hansen and Denis Thérien
In: 6th International Computer Science Symposium in Russia (CSR 2011), 14-18 june 2011, Saint Petersburg, Russia.

Abstract

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.

EPrint Type:Conference or Workshop Item (Paper)
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Theory & Algorithms
ID Code:9062
Deposited By:Ricard Gavaldà
Deposited On:21 February 2012