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Hardness Results for Intersection Non-Emptiness

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Part of the Lecture Notes in Computer Science book series (LNTCS,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

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Wehar, M. (2014). Hardness Results for Intersection Non-Emptiness. In: Esparza, J., Fraigniaud, P., Husfeldt, T., Koutsoupias, E. (eds) Automata, Languages, and Programming. ICALP 2014. Lecture Notes in Computer Science, vol 8573. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-43951-7_30

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  • DOI: https://doi.org/10.1007/978-3-662-43951-7_30

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-43950-0

  • Online ISBN: 978-3-662-43951-7

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