Predicting {0,1}-functions on randomly drawn points
COLT '88 Proceedings of the first annual workshop on Computational learning theory
A training algorithm for optimal margin classifiers
COLT '92 Proceedings of the fifth annual workshop on Computational learning theory
The minimum consistent DFA problem cannot be approximated within any polynomial
Journal of the ACM (JACM)
Efficient learning of typical finite automata from random walks
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
An introduction to computational learning theory
An introduction to computational learning theory
Machine Learning
Formal languages: an introduction and a synopsis
Handbook of formal languages, vol. 1
On the learnability and usage of acyclic probabilistic finite automata
Journal of Computer and System Sciences - Special issue on the eighth annual workshop on computational learning theory, July 5–8, 1995
Generalization performance of support vector machines and other pattern classifiers
Advances in kernel methods
Inference of Reversible Languages
Journal of the ACM (JACM)
Learning Subsequential Transducers for Pattern Recognition Interpretation Tasks
IEEE Transactions on Pattern Analysis and Machine Intelligence
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
Rational Kernels: Theory and Algorithms
The Journal of Machine Learning Research
Kernel methods for learning languages
Theoretical Computer Science
Learning languages with rational kernels
COLT'07 Proceedings of the 20th annual conference on Learning theory
Some Alternatives to Parikh Matrices Using String Kernels
Fundamenta Informaticae
On the learnability of shuffle ideals
ALT'12 Proceedings of the 23rd international conference on Algorithmic Learning Theory
On the learnability of shuffle ideals
The Journal of Machine Learning Research
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This paper presents a novel paradigm for learning languages that consists of mapping strings to an appropriate high-dimensional feature space and learning a separating hyperplane in that space. It initiates the study of the linear separability of automata and languages by examining the rich class of piecewise-testable languages. It introduces a high-dimensional feature map and proves piecewise-testable languages to be linearly separable in that space. The proof makes use of word combinatorial results relating to subsequences. It also shows that the positive definite kernel associated to this embedding can be computed in quadratic time. It examines the use of support vector machines in combination with this kernel to determine a separating hyperplane and the corresponding learning guarantees. It also proves that all languages linearly separable under a regular finite cover embedding, a generalization of the embedding we used, are regular.