An optimal parallel algorithm for learning DFA

Authors:
José L. Balcázar;Josep Díaz;Ricard Gavaldà;Osamu Watanabe
Affiliations:
Department of Software (L.S.I.), Univ. Politècnica de Catalunya, Pau Gargallo 5, 08028 Barcelona, Spain;Department of Software (L.S.I.), Univ. Politècnica de Catalunya, Pau Gargallo 5, 08028 Barcelona, Spain;Department of Software (L.S.I.), Univ. Politècnica de Catalunya, Pau Gargallo 5, 08028 Barcelona, Spain;Department of Computer Science, Tokyo Institute of Technology, Meguro-ku, Tokyo 152, Japan
Venue:
COLT '94 Proceedings of the seventh annual conference on Computational learning theory
Year:
1994

Citing 13
Cited 6

A theory of the learnable

Communications of the ACM
Learning regular sets from queries and counterexamples

Information and Computation
Inference of finite automata using homing sequences

STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Learning in parallel

COLT '88 Proceedings of the first annual workshop on Computational learning theory
Parallel algorithms for shared-memory machines

Handbook of theoretical computer science (vol. A)
An introduction to parallel algorithms

An introduction to parallel algorithms
The design and analysis of efficient learning algorithms

The design and analysis of efficient learning algorithms
Asking questions to minimize errors

COLT '93 Proceedings of the sixth annual conference on Computational learning theory
A framework for polynomial-time query learnability

Mathematical Systems Theory
Introduction To Automata Theory, Languages, And Computation

Introduction To Automata Theory, Languages, And Computation
Queries and Concept Learning

Machine Learning
Queries and Concept Learning

Machine Learning
A Note on the Query Complexity of Learning DFA (Extended Abstract)

ALT '92 Proceedings of the Third Workshop on Algorithmic Learning Theory

Noise-tolerant parallel learning of geometric concepts

COLT '95 Proceedings of the eighth annual conference on Computational learning theory
Exact Learning of Formulas in Parallel

Machine Learning
Cryptographic limitations on parallelizing membership and equivalence queries with applications to random-self-reductions

Theoretical Computer Science - Algorithmic learning theory
Cryptographic Limitations on Parallelizing Membership and Equivalence Queries with Applications to Random Self-Reductions

ALT '98 Proceedings of the 9th International Conference on Algorithmic Learning Theory
A bibliographical study of grammatical inference

Pattern Recognition
Zulu: an interactive learning competition

FSMNLP'09 Proceedings of the 8th international conference on Finite-state methods and natural language processing

Quantified Score

Hi-index	0.00

Visualization

Abstract

Sequential algorithms given by Alguin (1987) and Schapire (1992) learn deterministic finite automata (dfa) exactly from Membership and Equivalence queries. These algorithms are feasible, in the sense that they take time polynomial in n and m, where n is the number of states of the automaton and m is the length of the longest counterexample to an Equivalence query. This paper studies whether parallelism can lead to substantially more efficient algorithms for the problem. We show that no CRCW PRAM machine using a number of processors polynomial in n and m can identify dfa in o(n/logn) time. Furthermore, this lower bound is tight up to constant factors: we develop a CRCW PRAM learning algorithm that uses polynomially many processors and exactly learns dfa in time O(n/logn).