Abstract
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.
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© 1985 Springer-Verlag Berlin Heidelberg
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H.Ibarra, O., Ravikumar, B. (1985). On sparseness, ambiguity and other decision problems for acceptors and transducers. In: Monien, B., Vidal-Naquet, G. (eds) STACS 86. STACS 1986. Lecture Notes in Computer Science, vol 210. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-16078-7_74
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DOI: https://doi.org/10.1007/3-540-16078-7_74
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