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On Optimal Language Compression for Sets in PSPACE/poly

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We show that if DTIME[2O(n)] is not included in DSPACE[2o(n)], then, for every set B in PSPACE/poly, all strings x in B of length n can be represented by a string compressed(x) of length at most log(|B =n|)+O(log n), such that a polynomial-time algorithm, given compressed(x), can distinguish x from all the other strings in B =n. Modulo the O(log n) additive term, this achieves the information-theoretic optimum for string compression. We also observe that optimal compression is not possible for sets more complex than PSPACE/poly because for any time-constructible superpolynomial function t, there is a set A computable in space t(n) such that at least one string x of length n requires compressed(x) to be of length 2 log(|A =n|).

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Authors and Affiliations

  1. Department of Computer Science and Engineering, University of Nebraska-Lincoln, Lincoln, NE, USA

    N. V. Vinodchandran

  2. Department of Computer and Information Sciences, Towson University, Baltimore, MD, USA

    Marius Zimand

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  1. N. V. Vinodchandran
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  2. Marius Zimand
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Correspondence to Marius Zimand.

Additional information

Previous versions of this work have been presented at FCT’2011 and CCR’2012.

Part of the work was done while at Department of Computer Science, Johns Hopkins University. This work is supported in part by NSF grant CCF 0916525 (N. V. Vinodchandran).

This work is supported in part by NSF grant CCF 1016158 (Marius Zimand).

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Vinodchandran, N.V., Zimand, M. On Optimal Language Compression for Sets in PSPACE/poly. Theory Comput Syst 56, 581–590 (2015). https://doi.org/10.1007/s00224-014-9535-y

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  • DOI: https://doi.org/10.1007/s00224-014-9535-y

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