CSR 2011: Computer Science – Theory and Applications pp 29-42 | Cite as
Learning Read-Constant Polynomials of Constant Degree Modulo Composites
Conference paper
Abstract
Boolean functions that have constant degree polynomial representation over a fixed finite ring form a natural and strict subclass of the complexity class \(\text{ACC}^0\). They are also precisely the functions computable efficiently by programs over fixed and finite 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 finite rings from membership queries, with the additional constraint that each variable in the target polynomial appears in a constant number of monomials. Our algorithm extends to superconstant but low degree polynomials and still runs in quasipolynomial time.
Keywords
Boolean Function Nilpotent Group Pseudorandom Generator Membership Query Constant Degree
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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