From LL-Regular to LL (1) Grammars: Transformations, Covers and Parsing

Expressive Power of LL(k) Boolean Grammars

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 {anb2n | n > 0} non-representable. It is also shown that linear con...

Tests for the LR-, LL-, and LC-Regular Conditions

Most of the linear time parsing strategies (e.g., LL(k) and U(k) type parsers) for context-free grammars operate by looking ahead on the input tape for a fixed number of symbols. The fixed length look-ahead strings partition the set of input strings into classes of strings which are equivalent with respect to parsing decisions. A moment’s thought shows that these look-ahead classes are regular ...

On the Parsing of LL-Regular Grammars

Ch(k) Grammars: A Characterization of LL(k) Languages

From the point of view of parsing the LL(K] grammars constitute a very attractive class of context-free grammars. For each LL{K] grammar a top-down parsing algorithm can be devised which is essentially a one-state deterministic push-down automaton. From a more theoretiG point of view LL[K) grammars are attractive as well. It is well-known, for example, that it is decidable whether two LLfk) gra...

Simple Chain Grammars

A subclass of the LR(0)-grammars, the class of simple chain grammars is introduced. Although there exist simple chain gr~ars which are not LL(k) for any k, this new class of grammars is very close related to the class of LL(1) and simple LL(1) grammars. In fact it can be proved (not in this paper) that each simple chain grammar has an equivalent simple LL(1) grammar. A very simple (bottom-up) p...