TR#:  MSC200714 
Class:  MSC 
Title:  On Optimal Learning Algorithms for Multiplicity Automata 
Authors:  Laurence S. Bisht 
Supervisors:  Nader H. Bshouty 
MSC200714.pdf  
Abstract:  In computational learning theory, learning the class Multiplicity
Automata (MA) and Multiplicity Automata Function (MAF) over any
field from membership (substitution) and equivalence queries is
considered one of the most interesting problems studied in the
literature. This class includes many interesting classes such as:
decision trees, disjoint DNF, O(log n)term DNF, multivariate
polynomials, DFA, boxes and more.
We study polynomial time learning algorithms for Multiplicity
Automata (MA) and Multiplicity Automata Function (MAF).
We introduce efficient algorithms in several conditions. Our focus
is to minimize the access to one or more of the following resources:
Equivalence queries, Membership queries or Arithmetic operations
in the field.
This is in particular interesting when access to one or more of the
above resources is significantly more expensive than the others.
We apply new algebraic approach based on Matrix Theory to simplify the algorithms and the proofs of their correctness. We improve the arithmetic complexity of the problem and argue that it is almost optimal. Then we prove tight bound for the minimal number of equivalence queries and show an algorithm that achieves the bound. Regarding membership queries we prove almost (up to log factor) tight bound for the number of membership queries needed to learn MA.

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