Finding the Growth Rate of a Regular of Context-Free Language in Polynomial Time

  • Paweł Gawrychowski
  • Dalia Krieger
  • Narad Rampersad
  • Jeffrey Shallit
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5257)


We give an O(n + t) time algorithm to determine whether an NFA with n states and t transitions accepts a language of polynomial or exponential growth. Given a NFA accepting a language of polynomial growth, we can also determine the order of polynomial growth in O(n + t) time. We also give polynomial time algorithms to solve these problems for context-free grammars.


Polynomial Time Regular Language Polynomial Growth Jordan Block Primitive Root 
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 2008

Authors and Affiliations

  • Paweł Gawrychowski
    • 1
  • Dalia Krieger
    • 2
  • Narad Rampersad
    • 2
  • Jeffrey Shallit
    • 2
  1. 1.Institute of Computer ScienceUniversity of WrocławWrocławPoland
  2. 2.School of Computer ScienceUniversity of WaterlooWaterlooCanada

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