An Infinite Automaton Characterization of Double Exponential Time

  • Authors:
  • Salvatore Torre;P. Madhusudan;Gennaro Parlato

  • Affiliations:
  • Università di Salerno, Italy;University of Illinois, Urbana-Champaign, USA;Università di Salerno, Italy and University of Illinois, Urbana-Champaign, USA

  • Venue:
  • CSL '08 Proceedings of the 22nd international workshop on Computer Science Logic
  • Year:
  • 2008

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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 2ETimeis obvious. In this sense, the result captures the complexity class qualitatively, by restricting the power of rewriting.