Observations on log(n) time parallel recognition of unambiguous CFL's
Information Processing Letters
Semirings and formal power series: their relevance to formal languages and automata
Handbook of formal languages, vol. 1
Journal of the ACM (JACM)
Journal of the ACM (JACM)
Introduction To Automata Theory, Languages, And Computation
Introduction To Automata Theory, Languages, And Computation
Introduction to Formal Language Theory
Introduction to Formal Language Theory
Automata: Theoretic Aspects of Formal Power Series
Automata: Theoretic Aspects of Formal Power Series
The Theory of Parsing, Translation, and Compiling
The Theory of Parsing, Translation, and Compiling
Universal Inherence of Cycle-Free Context-Free Ambiguity Functions
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
On the number of occurrences of a symbol in words of regular languages
Theoretical Computer Science
An efficient context-free parsing algorithm
An efficient context-free parsing algorithm
Information and Computation
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Context-free grammars and languages with infinite ambiguity can be distinguished by the growth rate of their ambiguity with respect to the length of the words. So far the least growth rate known for a divergent inherent ambiguity function was logarithmic. Roughly speaking we show that it is possible to stay below any computable function. More precisely let f : N → N be an arbitrary computable divergent total non-decreasing function. Then there is a context-free language L with a divergent inherent ambiguity function g below f, i.e., g(n) ≤ f(n) for each n ∈ N. This result is an immediate consequence of two other results which are of independent interest. The first result says that there is a linear context-free grammar G with so called unambiguous turn position whose ambiguity function is below f. The second one states that any ambiguity function of a cycle-free context-free grammar is an inherent ambiguity function of some context-free language.