An Infinite Automaton Characterization of Double Exponential Time

  • Salvatore La Torre
  • P. Madhusudan
  • Gennaro Parlato
Conference paper

DOI: 10.1007/978-3-540-87531-4_5

Part of the Lecture Notes in Computer Science book series (LNCS, volume 5213)
Cite this paper as:
La Torre S., Madhusudan P., Parlato G. (2008) An Infinite Automaton Characterization of Double Exponential Time. In: Kaminski M., Martini S. (eds) Computer Science Logic. CSL 2008. Lecture Notes in Computer Science, vol 5213. Springer, Berlin, Heidelberg

Abstract

Infinite-state automata are a new invention: they are automata that have an infinite number of states represented by words, transitions defined using rewriting, and with sets of initial and final states. Infinite-state automata have gained recent interest due to a remarkable result by Morvan and Stirling, which shows that automata with transitions defined using rational rewriting precisely capture context-sensitive (NLinSpace) languages. In this paper, we show that infinite automata defined using a form of multi-stack rewriting precisely defines double exponential time (more precisely, 2ETime, the class of problems solvable in \(2^{2^{O(n)}}\) time). The salient aspect of this characterization is that the automata have no ostensible limits on time nor space, and neither direction of containment with respect to 2ETime is obvious. In this sense, the result captures the complexity class qualitatively, by restricting the power of rewriting.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Salvatore La Torre
    • 1
  • P. Madhusudan
    • 2
  • Gennaro Parlato
    • 1
    • 2
  1. 1.Università di SalernoItaly
  2. 2.University of IllinoisUrbana-ChampaignUSA

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