The complexity of learning SUBSEQ(A)

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 lexicographic enumeration of all strings over some finite alphabet. We consider the following inductive inference problem: given 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, mindchanges, teams, and combinations thereof. This paper is a significant revision and expansion of an earlier conference version [10].

• Type: Journal
• Year: 2008
• Where: ECCC
• Authors: Stephen A. Fenner, William I. Gasarch, Brian Postow
• Keywords: ECCC 2008, Finite Alphabet, Inductive Inference, Standard Lexicographic Enumeration