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

- First Online:

DOI: 10.1007/3-540-16078-7_74

- 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

## 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*)=Σ*a*_{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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