Communications of the ACM
Learning regular sets from queries and counterexamples
Information and Computation
Rational series and their languages
Rational series and their languages
A deterministic algorithm for sparse multivariate polynomial interpolation
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Interpolating polynomials from their values
Journal of Symbolic Computation - Special issue on computational algebraic complexity
Introduction to algorithms
Fast parallel algorithms for sparse multivariate polynomial interpolation over finite fields
SIAM Journal on Computing
Interpolation and approximation of sparse multivariate polynomials over GF(2)
SIAM Journal on Computing
Learning 2u DNF formulas and ku decision trees
COLT '91 Proceedings of the fourth annual workshop on Computational learning theory
Handbook of theoretical computer science (vol. A)
On zero-testing and interpolation of k -sparse multivariate polynomials over finite fields
Theoretical Computer Science
Exact learning of read-twice DNF formulas (extended abstract)
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
On-line learning of rectangles
COLT '92 Proceedings of the fifth annual workshop on Computational learning theory
Random DFA's can be approximately learned from sparse uniform examples
COLT '92 Proceedings of the fifth annual workshop on Computational learning theory
Exact learning of read-k disjoint DNF and not-so-disjoint DNF
COLT '92 Proceedings of the fifth annual workshop on Computational learning theory
Learning read-once formulas with queries
Journal of the ACM (JACM)
C4.5: programs for machine learning
C4.5: programs for machine learning
Learning decision trees using the Fourier spectrum
SIAM Journal on Computing
Cryptographic hardness of distribution-specific learning
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
On-line learning of rectangles in noisy environments
COLT '93 Proceedings of the sixth annual conference on Computational learning theory
Cryptographic limitations on learning Boolean formulae and finite automata
Journal of the ACM (JACM)
Inference of finite automata using homing sequences
Information and Computation
On learning Read-k-Satisfy-j DNF
COLT '94 Proceedings of the seventh annual conference on Computational learning theory
Learning unions of boxes with membership and equivalence queries
COLT '94 Proceedings of the seventh annual conference on Computational learning theory
An introduction to computational learning theory
An introduction to computational learning theory
Read-twice DNF formulas are properly learnable
Information and Computation
Fast learning of k-term DNF formulas with queries
Journal of Computer and System Sciences - Special issue on selected papers presented at the 24th annual ACM symposium on the theory of computing (STOC '92)
Exact learning Boolean functions via the monotone theory
Information and Computation
A note on learning multivariate polynomials under the uniform distribution (extended abstract)
COLT '95 Proceedings of the eighth annual conference on Computational learning theory
Learning sparse multivariate polynomials over a field with queries and counterexamples
Journal of Computer and System Sciences
Learning Sat-k-DNF formulas from membership queries
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Learning Behaviors of Automata from Multiplicity and Equivalence Queries
SIAM Journal on Computing
Simple learning algorithms using divide and conquer
Computational Complexity
A simple algorithm for learning O (log n)-term DNF
Information Processing Letters
Communication complexity
An efficient membership-query algorithm for learning DNF with respect to the uniform distribution
Journal of Computer and System Sciences
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Efficient learning with virtual threshold gates
Information and Computation
Interpolation of sparse multivariate polynomials over large finite fields with applications
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
Fast Probabilistic Algorithms for Verification of Polynomial Identities
Journal of the ACM (JACM)
Automata, Languages, and Machines
Automata, Languages, and Machines
Machine Learning
Machine Learning
Machine Learning
Probabilistic algorithms for sparse polynomials
EUROSAM '79 Proceedings of the International Symposiumon on Symbolic and Algebraic Computation
Learning behaviors of automata from shortest counterexamples
EuroCOLT '95 Proceedings of the Second European Conference on Computational Learning Theory
Simple learning algorithms for decision trees and multivariate polynomials
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
On the applications of multiplicity automata in learning
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
SIGACT News complexity theory column 32
ACM SIGACT News
Learning Expressions over Monoids
STACS '01 Proceedings of the 18th Annual Symposium on Theoretical Aspects of Computer Science
On the Proper Learning of Axis Parallel Concepts
COLT '02 Proceedings of the 15th Annual Conference on Computational Learning Theory
On the proper learning of axis-parallel concepts
The Journal of Machine Learning Research
Learning expressions and programs over monoids
Information and Computation
Interpolation of depth-3 arithmetic circuits with two multiplication gates
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Agnostically learning decision trees
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
ALT '08 Proceedings of the 19th international conference on Algorithmic Learning Theory
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
Cryptographic hardness for learning intersections of halfspaces
Journal of Computer and System Sciences
Property Testing: A Learning Theory Perspective
Foundations and Trends® in Machine Learning
Grammatical inference as a principal component analysis problem
ICML '09 Proceedings of the 26th Annual International Conference on Machine Learning
Definable transductions and weighted logics for texts
Theoretical Computer Science
Learning expressions and programs over monoids
Information and Computation
An algebraic perspective on Boolean function learning
ALT'09 Proceedings of the 20th international conference on Algorithmic learning theory
Arithmetic Circuits: A survey of recent results and open questions
Foundations and Trends® in Theoretical Computer Science
Learning read-constant polynomials of constant degree modulo composites
CSR'11 Proceedings of the 6th international conference on Computer science: theory and applications
On optimal learning algorithms for multiplicity automata
COLT'06 Proceedings of the 19th annual conference on Learning Theory
Learning rational stochastic languages
COLT'06 Proceedings of the 19th annual conference on Learning Theory
On PAC learning algorithms for rich boolean function classes
TAMC'06 Proceedings of the Third international conference on Theory and Applications of Models of Computation
Ten open problems in grammatical inference
ICGI'06 Proceedings of the 8th international conference on Grammatical Inference: algorithms and applications
Learning multiplicity tree automata
ICGI'06 Proceedings of the 8th international conference on Grammatical Inference: algorithms and applications
On identity testing of tensors, low-rank recovery and compressed sensing
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Reconstruction of depth-4 multilinear circuits with top fan-in 2
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Learning Probabilistic Systems from Tree Samples
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
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We study the learnability of multiplicity automata in Angluin's exact learning model, and we investigate its applications. Our starting point is a known theorem from automata theory relating the number of states in a minimal multiplicity automaton for a function to the rank of its Hankel matrix. With this theorem in hand, we present a new simple algorithm for learning multiplicity automata with improved time and query complexity, and we prove the learnability of various concept classes. These include (among others): -The class of disjoint DNF, and more generally satisfy-O(1) DNF.-The class of polynomials over finite fields.-The class of bounded-degree polynomials over infinite fields.-The class of XOR of terms.-Certain classes of boxes in high dimensions.In addition, we obtain the best query complexity for several classes known to be learnable by other methods such as decision trees and polynomials over GF(2).While multiplicity automata are shown to be useful to prove the learnability of some subclasses of DNF formulae and various other classes, we study the limitations of this method. We prove that this method cannot be used to resolve the learnability of some other open problems such as the learnability of general DNF formulas or even k-term DNF for k = &ohgr;(log n) or satisfy-s DNF formulas for s = &ohgr;(1). These results are proven by exhibiting functions in the above classes that require multiplicity automata with super-polynomial number of states.