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On the Complexity of Intersecting Regular, Context-Free, and Tree Languages

  • Joseph Swernofsky
  • Michael Wehar
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9135)

Abstract

We apply a construction of Cook (1971) to show that the intersection non-emptiness problem for one PDA (pushdown automaton) and a finite list of DFA’s (deterministic finite automata) characterizes the complexity class P. In particular, we show that there exist constants \(c_1\) and \(c_2\) such that for every k, intersection non-emptiness for one PDA and k DFA’s is solvable in \(O(n^{c_1 k})\) time, but is not solvable in \(O(n^{c_2 k})\) time. Then, for every k, we reduce intersection non-emptiness for one PDA and \(2^k\) DFA’s to non-emptiness for multi-stack pushdown automata with k-phase switches to obtain a tight time complexity lower bound. Further, we revisit a construction of Veanes (1997) to show that the intersection non-emptiness problem for tree automata also characterizes the complexity class P. We show that there exist constants \(c_1\) and \(c_2\) such that for every k, intersection non-emptiness for k tree automata is solvable in \(O(n^{c_1 k})\) time, but is not solvable in \(O(n^{c_2 k})\) time.

Keywords

Turing Machine Input String Tree Automaton Input Position Acceptance Problem 
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 2015

Authors and Affiliations

  1. 1.Independent ResearcherLos AltosUSA
  2. 2.University at BuffaloBuffaloUSA

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