LR Parsing for Boolean Grammars

Generalized Lr Parsing Algorithm for Boolean Grammars

“…For the case of conjunctive grammars [10] it is known that if u ∈ L G + (s), then F irst k (u) ∈ Pfirst k (s), which immediately implies the correctness of Algorithm 1. Algorithm 2 For a given Boolean grammar G compliant to the semantics of naturally reachable solution and for k > 0, compute the sets Pfollow…”

“…Now, for every nonterminal A ∈ N , define First k (A) = F irst k (L G (A)) and Follow k (A) = {F irst k (u) | u follows A}. Already for conjunctive grammars there cannot exist an algorithm to compute the sets First k and Follow k precisely [10]: this is an easy consequence of the undecidability of the emptiness problem [9]. However, since the LR algorithm uses the lookahead information solely to eliminate some superfluous reductions, if the sets First k (A) and Follow k (A) are replaced by some of their supersets, the resulting LR parser will still work, though it will have to spend extra time doing some computations that will not influence the result.…”

“…The new LR parsing algorithm for Boolean grammars is a generalization of the corresponding algorithm for conjunctive grammars [10], which is in turn based upon a variant of Tomita's algorithm [19] for context-free grammars. This section gives a general description of the new algorithm, emphasizing its difference from its prototypes.…”

“…The new algorithm is partially based upon the author's earlier attempt to extend the applicability of the Generalized LR to conjunctive grammars [10]. Conjunctive grammars [9] are, to put it simply, context-free grammars with added conjunction, or, in other words, Boolean grammars without negation.…”

“…Their expressive power is still quite greater than that of the context-free grammars. Generalized LR parsing can be extended to these grammars rather straightforwardly, and its worst-case complexity is still only cubic [10].…”