Descriptive Complexity, Lower Bounds and Linear Time

  • Thomas Schwentick
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1584)

Abstract

This paper surveys two related lines of research:
  • Logical characterizations of (non-deterministic) linear time complexity classes, and

  • non-expressibility results concerning sublogics of existential second-order logic.

Starting from Fagin’s fundamental work there has been steady progress in both fields with the effect that the weakest logics that are used in characterizations of linear time complexity classes are closely related to the strongest logics for which inexpressibility proofs for concrete problems have been obtained. The paper sketches these developments and highlights their connections as well as the obstacles that prevent us from closing the remaining gap between both kinds of logics.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Thomas Schwentick
    • 1
  1. 1.Johannes Gutenberg-Universität Mainz 

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