Abstract

The paper studies the family of Boolean LL languages, generated by Boolean grammars and usable with the recursive descent parsing. It is demonstrated that over a one-letter alphabet, these languages are always regular, while Boolean LL subsets of Σ ∗ a ∗ obey a certain periodicity property, which, in particular, makes the language { a n b 2 n | n ⩾ 0 } non-representable. It is also shown that linear conjunctive LL grammars cannot generate any language of the form L ⋅ { a , b } , with L non-regular, and that no languages of the form L ⋅ c ∗ , with non-regular L , can be generated by any linear Boolean LL grammars. These results are used to establish a detailed hierarchy and closure properties of these and related families of formal languages.

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