Parekh, Rajesh and Honavar, Vasant (1995) An Efficient Interactive Algorithm for Regular Language Learning. Technical Report TR95-02, Department of Computer Science, Iowa State University.
An Efficient Interactive Algorithm for Regular Language Learning
Rajesh Parekh & Vasant Honavar
Artificial Intelligence Research Group
ISU CS-TR 95-02
Department of Computer Science
226 Atanasoff Hall,
Iowa State University,
Ames, IA 50011. U.S.A.
This paper presents an efficient algorithm for learning regular grammars.
A knowledgeable teacher provides the learner with a structurally complete
set of strings that belong to L(G), the language corresponding to an unknown
regular grammar G. This structurally complete set of positive examples
implicitly specifies a lattice which represents the hypothesis space of
candidate grammars that contains the unknown grammar G. The learner searches
this lattice by posing queries about the membership in G of particular strings
and uses the teacher's response to eliminate parts of the hypothesis space.
The learner maintains at all time, a compact representation of the lattice
in the form of two sets $\cal S$ and $\cal G$ that correspond (respectively)
to the set of most specific and most general grammars consistent with the set
of positive examples provided and the queries answered by the teacher up to
that point in time. The correctness of the algorithm is established by
proving that at least one element of the lattice, G*, that is equivalent to
the unknown grammar G, is contained in the hypothesis space represented by
$\cal S$ and $\cal G$ and that the algorithm terminates upon identifying such
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