On sparseness, ambiguity and other decision problems for acceptors and transducers
- Cite this paper as:
- H.Ibarra O., Ravikumar B. (1986) 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
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 fL(z)=Σanzn, where an 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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