Lower bounds on the size of sweeping automata

  • Authors:
  • Juraj Hromkovič;Georg Schnitger

  • Affiliations:
  • Department of Computer Science, ETH Zürich, ETH Zentrum, Zürich, Switzerland;Institute of Computer Science, Johann Wolfgang Goethe Universität, Frankfurt a. M., Germany

  • Venue:
  • Journal of Automata, Languages and Combinatorics
  • Year:
  • 2009

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Abstract

A deterministic sweeping automaton is a two-way deterministic automaton (2-DFA) which makes turns only at the left or right end of the input. We give a survey on recent lower bounds for the conciseness of sweeping automata. We also show that any sweeping automaton for the language (L$)* has to have at least √m/2 states whenever the nondeterministic message complexity of L is at least m. Thus we obtain the first general method to establish lower bounds on the conciseness of sweeping automata.