Proactive password checking with decision trees
Proceedings of the 4th ACM conference on Computer and communications security
The query complexity of finding local minima in the lattice
COLT' 98 Proceedings of the eleventh annual conference on Computational learning theory
On learning in the presence of unspecified attribute values
COLT '99 Proceedings of the twelfth annual conference on Computational learning theory
Learning functions represented as multiplicity automata
Journal of the ACM (JACM)
The query complexity of finding local minima in the lattice
Information and Computation
Exact learning of DNF formulas using DNF hypotheses
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Learning Multiplicity Automata from Smallest Counterexamples
EuroCOLT '99 Proceedings of the 4th European Conference on Computational Learning Theory
Learning Unary Output Two-Tape Automata from Multiplicity and Equivalence Queries
ALT '98 Proceedings of the 9th International Conference on Algorithmic Learning Theory
Learning Regular Sets with an Incomplete Membership Oracle
COLT '01/EuroCOLT '01 Proceedings of the 14th Annual Conference on Computational Learning Theory and and 5th European Conference on Computational Learning Theory
On Learning Monotone DNF under Product Distributions
COLT '01/EuroCOLT '01 Proceedings of the 14th Annual Conference on Computational Learning Theory and and 5th European Conference on Computational Learning Theory
Pseudorandom functions in TC0 and cryptographic limitations to proving lower bounds
Computational Complexity
Learning intersections and thresholds of halfspaces
Journal of Computer and System Sciences - Special issue on FOCS 2002
Exact learning of DNF formulas using DNF hypotheses
Journal of Computer and System Sciences - Special issue on COLT 2002
Using Multiplicity Automata to Identify Transducer Relations from Membership and Equivalence Queries
ICGI '08 Proceedings of the 9th international colloquium on Grammatical Inference: Algorithms and Applications
Efficient learning algorithms yield circuit lower bounds
Journal of Computer and System Sciences
Learning rational stochastic languages
COLT'06 Proceedings of the 19th annual conference on Learning Theory
Efficient learning algorithms yield circuit lower bounds
COLT'06 Proceedings of the 19th annual conference on Learning Theory
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The learnability of multiplicity automata has attracted a lot of attention, mainly because of its implications on the learnability of several classes of DNF formulae. The authors further study the learnability of multiplicity automata. The starting point is a known theorem from automata theory relating the number of states in a minimal multiplicity automaton for a function f to the rank of a certain matrix F. With this theorem in hand they obtain the following results: a new simple algorithm for learning multiplicity automata with a better query complexity. As a result, they improve the complexity for all classes that use the algorithms of Bergadano and Varricchio (1994) and Ohnishi et al. (1994) and also obtain the best query complexity for several classes known to be learnable by other methods such as decision trees and polynomials over GF(2). They prove the learnability of some new classes that were not known to be learnable before. Most notably, the class of polynomials over finite fields, the class of bounded-degree polynomials over infinite fields, the class of XOR of terms, and a certain class of decision trees. While multiplicity automata were shown to be useful to prove the learnability of some subclasses of DNF formulae and various other classes, they study the limitations of this method. They prove that this method cannot be used to resolve the learnability of some other open problems such as the learnability of general DNF formulae or even K-term DNF for k=/spl omega/ (log n) or satisfy-s DNF formulae for s=/spl omega/(1). These results are proven by exhibiting functions in the above classes that require multiplicity automata with superpolynomial number of states.