A new top-down parsing algorithm to accommodate ambiguity and left recursion in polynomial time

Abstract

Top-down backtracking language processors are highly modular, can handle ambiguity, and are easy to implement with clear and maintainable code. However, a widely-held, and incorrect, view is that top-down processors are inherently exponential for ambiguous grammars and cannot accommodate left-recursive productions. It has been known for many years that exponential complexity can be avoided by memoization, and that left-recursive productions can be accommodated through a variety of techniques. However, until now, memoization and techniques for handling left recursion have either been presented independently, or else attempts at their integration have compromised modularity and clarity of the code.

Joint learning of ontology and semantic parser from text

“…For each of the term -non-terminal pair in every list the parse function is recursively called (line 10). for i ← 0 to size of term list do 10 child node ← Parse(term list i , pattern.non terminals i ) ; 11 add child node to child nodes; 12 add Node(type, p , r, child nodes) to nodes; 13 if nodes is empty then 14 final node ← Node(type, p , null, {}); 15 else 16 final node ← arg max n∈nodes r(n) ; 17 if final node is not fully parsed then 18 add final node to induction nodes ; 19 return final node Algorithm 1: Pseudocode of the main function parse of the top-down parser.…”

Language Parsing and Syntax of Malayalam Language

“…A probabilistic method has been tried for parsing natural language sentences [3,4]. A top-down parsing algorithm to accommodate ambiguity and left recursion in polynomial time has also been tried [5]. A shift reduce parsing technique has been used for word sense disambiguation [6].…”

Parsing with derivatives

“…The work applies Brzozowski's work on derivatives for regular languages [4] to context-free languages as a new method of parsing. Parsing with derivatives can be used to construct parser combinator libraries that can parse arbitrary context-free grammars, which is usually complicated (see for example [8]).…”

“…It is therefore of interest to have methods that allow parsing such grammars, and preferably using simple algorithms. Parser combinator libraries can be implemented to handle left-recursion, [8] but these do not follow from a clear mathematical theory, and in turn their correctness is harder to prove.…”