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The Complexity of Finding SUBSEQ(A)

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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).

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Authors and Affiliations

  1. Department of Computer Science and Engineering, University of South Carolina, Columbia, SC, 29208, USA

    Stephen Fenner

  2. Dept. of Computer Science and Institute for Advanced Computer Studies, University of Maryland, College Park, MD, 20742, USA

    William Gasarch

  3. Department of Computer Science, Union College, Schenectady, NY, 12308, USA

    Brian Postow

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  1. Stephen Fenner
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  2. William Gasarch
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  3. Brian Postow
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Correspondence to Stephen Fenner.

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Fenner, S., Gasarch, W. & Postow, B. The Complexity of Finding SUBSEQ(A). Theory Comput Syst 45, 577–612 (2009). https://doi.org/10.1007/s00224-008-9111-4

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