On the Gap-Complexity of Simple RL-Automata

  • F. Mráz
  • F. Otto
  • M. Plátek
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4036)


Analysis by reduction is a method used in linguistics for checking the correctness of sentences of natural languages. This method is modelled by restarting automata. Here we introduce and study a new type of restarting automaton, the so-called t- sRL -automaton, which is an RL-automaton that is rather restricted in that it has a window of size 1 only, and that it works under a minimal acceptance condition. On the other hand, it is allowed to perform up to t rewrite (that is, delete) steps per cycle. Here we study the gap-complexity of these automata. The membership problem for a language that is accepted by a t-sRL-automaton with a bounded number of gaps can be solved in polynomial time. On the other hand, t-sRL-automata with an unbounded number of gaps accept NP-complete languages.


Regular Language Initial Vertex Language Class Input Word Membership Problem 
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© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • F. Mráz
    • 1
  • F. Otto
    • 2
  • M. Plátek
    • 1
  1. 1.Faculty of Mathematics and Physics, Department of Computer ScienceCharles UniversityPraha 1Czech Republic
  2. 2.Fachbereich Mathematik/InformatikUniversität KasselKasselGermany

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