Kolmogorov complexity, restricted nondeterminism and generalized spectra

  • Deborah Joseph
  • Meera Sitharam
Conference paper

DOI: 10.1007/3-540-52282-4_39

Part of the Lecture Notes in Computer Science book series (LNCS, volume 415)
Cite this paper as:
Joseph D., Sitharam M. (1990) Kolmogorov complexity, restricted nondeterminism and generalized spectra. In: Choffrut C., Lengauer T. (eds) STACS 90. STACS 1990. Lecture Notes in Computer Science, vol 415. Springer, Berlin, Heidelberg

Abstract

This paper uses the technique of generalized spectra and expressibility of complexity classes in logic, developed by Fagin and Immerman, to give alternate characterizations of specific subclasses of NP. These characterizations serve to unify concepts that appear in seemingly different areas of complexity theory; namely, the restricted nondeterminism of Kintala and Fischer and the time bounded Kolmogorov complexity of Daley and Ko. As consequences of these characterizations we show that relatively easy subsets of NP−P can not be pseudorandomly generated, unless UTIME[t(n)]=DTIME[t(n)] for certain exponential functions t. Secondly, we show that no easy subset of the set of all satisfying assignments of satisfiable g(n)-easy formulas contains an assignment for each of these formulas, unless NEXPTIME = EXPTIME. The latter partially answers a question raised by Hartmanis.

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Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • Deborah Joseph
    • 1
  • Meera Sitharam
    • 1
  1. 1.Computer Sciences DepartmentUniversity of WisconsinMadisonUSA

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