The Complexity of Finding SUBSEQ(A)

Authors:
Stephen Fenner;William Gasarch;Brian Postow
Affiliations:
University of South Carolina, Department of Computer Science and Engineering, 29208, Columbia, SC, USA;University of Maryland, Dept. of Computer Science and Institute for Advanced Computer Studies, 20742, College Park, MD, USA;Union College, Department of Computer Science, 12308, Schenectady, NY, USA
Venue:
Theory of Computing Systems
Year:
2009

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Abstract

Higman showed that if A is any language then SUBSEQ(A) is regular. His proof was nonconstructive. We show that the result cannot be made constructive. In particular we show that if f takes as input an index e of a total Turing Machine M e , and outputs a DFA for SUBSEQ(L(M e )), then ∅″≤T f (f is Σ 2-hard). We also study the complexity of going from A to SUBSEQ(A) for several representations of A and SUBSEQ(A).