Hardness Results for Intersection Non-Emptiness

  • Michael Wehar
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8573)

Abstract

We carefully reexamine a construction of Karakostas, Lipton, and Viglas (2003) to show that the intersection non-emptiness problem for DFA’s (deterministic finite automata) characterizes the complexity class NL. In particular, if restricted to a binary work tape alphabet, then there exist constants c1 and c2 such that for every k intersection non-emptiness for k DFA’s is solvable in c1k log(n) space, but is not solvable in c2k log(n) space. We optimize the construction to show that for an arbitrary number of DFA’s intersection non-emptiness is not solvable in \(o(\frac{n}{\log(n)\log(\log(n))})\) space. Furthermore, if there exists a function f(k) = o(k) such that for every k intersection non-emptiness for k DFA’s is solvable in nf(k) time, then P ≠ NL. If there does not exist a constant c such that for every k intersection non-emptiness for k DFA’s is solvable in nc time, then P does not contain any space complexity class larger than NL.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Michael Wehar
    • 1
  1. 1.Department of Computer Science and EngineeringUniversity at BuffaloBuffaloUSA

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