Summary
Simple LR(1) and lookahead LR(1) phrase structure grammars are defined and corresponding deterministic two-pushdown automata which parse all sentences are given. These grammars include a wide variety of grammars for non context-free languages. A given phrase structure grammar is one of these types if the parse table for the associated automaton has no multiple entries. A technique for construction of this parse table is given which in the lookahead case involves elimination of inverses in a grammar for lookahead strings for LR(0) items and computation of first sets for strings of symbols in the given grammar.
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Harris, L.A. SLR(1) and LALR(1) parsing for unrestricted grammars. Acta Informatica 24, 191–209 (1987). https://doi.org/10.1007/BF00264364
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DOI: https://doi.org/10.1007/BF00264364