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The complexity of learning SUBSEQ(A)

Published online by Cambridge University Press:  12 March 2014

Stephen Fenner ,
William Gasarch  and
Brian Postow
Stephen Fenner
Affiliation:
Department of Computer Science and Engineering, University of South Carolina, Columbia, Sc 29208, USA, E-mail: fenner@cse.sc.edu
William Gasarch
Affiliation:
Department of Computer Science and Institute for Advanced Computer Studies, University of MarylandAt College Park, College Park, Md 20742, USA, E-mail: gasarch@cs.umd.edu
Brian Postow
Affiliation:
Acordex Imaging Systems, 37 Walker Road, North Andover, Ma 01845, USA, E-mail: postow@acm.org
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Abstract

Higman essentially showed that if A is any language then SUBSEQ(A) is regular, where SUBSEQ(A) is the language of all subsequences of strings in A. Let s1,s2,s3,… be the standard lexico-graphic enumeration of all strings over some finite alphabet. We consider the following inductive inference problem: A(s1),A(s2),A(s3),…, learn, in the limit, a DFA for SUBSEQ(A). We consider this model of learning and the variants of it that are usually studied in Inductive Inference: anomalies, mind-changes, teams, and combinations thereof.

This paper is a significant revision and expansion of an earlier conference version [10].

Keywords

machine learninginductive inferenceautomatacomputabilitysubsequence
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 74 , Issue 3 , September 2009 , pp. 939 - 975
Copyright
Copyright © Association for Symbolic Logic 2009

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