Enumeration of context-free languages and related structures

Authors:
Michael Domaratzki;Alexander Okhotin;Jeffrey Shallit
Affiliations:
Department of Computer Science, University of Manitoba, Winnipeg, Canada;Department of Mathematics, University of Turku, Turku, Finland and Academy of Finland;School of Computer Science, University of Waterloo, Waterloo, Ontario, Canada
Venue:
Journal of Automata, Languages and Combinatorics
Year:
2007

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Abstract

In this paper, we consider the enumeration of context-free languages. In particular, for any reasonable descriptional complexity measure for context-free grammars, we demonstrate that the exact number of context-free languages of size n is uncomputable. Nevertheless, we are able to give upper and lower bounds on the number of such languages. We also generalize our uncomputability results to a general theorem applicable to enumeration of equivalence classes or yes-instances of predicates.