On learning multivariate polynomials under the uniform distribution

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We present a PAC-learning algorithm with membership queries for learning any multivariate polynomial over any finite field F under the uniform distribution. The algorithm runs in polynomial time and asks t O(¦F ¦log¦F¦) log n queries where t is the number of terms in the polynomial, n is the number of variables and ¦F¦ is the field size. This complexity is polynomial for any fixed finite field F.The output hypothesis is a multivariate polynomial with at most t terms. We also show that O( log n)-multivariate polynomials (each term contains at most O( log n) variables) are exactly learnable from membership and equivalence queries in time n O(log¦F¦) .