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 .