On sparseness, ambiguity and other decision problems for acceptors and transducers

  • Oscar H.Ibarra
  • B. Ravikumar
Contributed Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 210)


We consider some decision problems on sparseness, degrees of ambiguity and multiple valuedness concerning finite-state and pushdown acceptors and transducers. A language L is sparse if there is a polynomial P such that the number of strings of length n in L is atmost P(n). A recognizer (transducer) is of polynomial ambiguity (valued) if there exists a polynomial P such that the number of derivations (outputs) for any input of length n is at most P(n). We relate these problems and show that they are decidable for finite-state devices. For cfl's, only the sparseness problem is decidable. We also study some properties of structure generating function defined as f L (z)=Σa n z n , where a n is the number of strings of length n in a language L. Our results are useful in proving the non-regularity/non-context-freeness of some languages.


Direct Derivation Growth Function Regular Language Straight Edge Ambiguity Function 
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 1985

Authors and Affiliations

  • Oscar H.Ibarra
    • 1
  • B. Ravikumar
    • 1
  1. 1.Department of Computer ScienceUniversity of MinnesotaMinneapolis

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