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Hardness Results for Intersection Non-Emptiness

Conference paper
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 c 1 and c 2 such that for every k intersection non-emptiness for k DFA’s is solvable in c 1 k log(n) space, but is not solvable in c 2 k 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 n f(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 n c time, then P does not contain any space complexity class larger than NL.

Keywords

Turing Machine Work Position Hardness Result Input String Tree Automaton 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Department of Computer Science and EngineeringUniversity at BuffaloBuffaloUSA

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