## The complexity of computing the number of strings of given length in context-free languages.(English)Zbl 0744.68066

For a context-free language $$L$$, $$f_ L(1^ n)$$ denotes the number of strings of length $$n$$ belonging to $$L$$. The counting function $$f_ L$$ is used to study the inherent ambiguity of the context-free languages and to solve enumeration problems.
The paper concerns with the complexity of computing of the counting function $$f_ L$$. The main result is proven in the second section and it claims that if $$L$$ is an unambiguous context-free language then $$f_ L$$ can be computed by a log-space uniform family of Boolean circuits with depth $$O(\log n\log\log n)$$ and polynomial size. The third and the fourth sections study the complexity of computing of the function $$f_ L$$ by counting Turing machines. In the last section is defined a language of ambiguity degree two for that the counting function $$f_ L$$ is $$\# P_ 1$$-complete ($$\# P_ 1$$ is the class of all functions $$f: \{1\}^*\to N$$ countable in polynomial time by a counting Turing machine).
Reviewer: D.Lucanu (Iaşi)

### MSC:

 68Q25 Analysis of algorithms and problem complexity 68W15 Distributed algorithms 68Q45 Formal languages and automata
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### References:

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