A top-down no backtrack parsing of general context-free languages

Abstract

A new parsing algorithm is presented. The algorithm works in a top-down manner and it is easily implementable. The algorithm works for all non left-recursive ε-free context-free grammars. For LR(1) left-recursion-free grammars works like an LR(1) push-down acceptor. The time bounds are O(n³) for all context-free grammars, O(n²) for a superset of unambiguous grammars and O(n) for a superset of LR grammars (see Graham, Harrison [1]). It is hoped that the ideas used in the algorithm can help to find an accepting algorithm working in time O(n²). The method has promising properties for error recovery in compilers and produces all the possible parses in a string encoding. In any case, the ideas presented in the paper can contribute to the understanding of the parsing problem of general context-free languages.