Generalised LR parsing algorithms

Giorgios R. Economopoulos. Generalised LR parsing algorithms. PhD thesis, Royal Holloway, University of London, August 2006.


This thesis concerns the parsing of context-free grammars. A parser is a tool, defined for a specific grammar, that constructs a syntactic representation of an input string and determines if the string is grammatically correct or not. An algorithm that is capable of parsing any context-free grammar is called a generalised (context-free) parser. This thesis is devoted to the theoretical analysis of generalised parsing algorithms. We describe, analyse and compare several algorithms that are based on Knuth’s LR parser. This work underpins the design and implementation of the Parser Animation Tool (PAT). We use PAT to evaluate the asymptotic complexity of generalised parsing algorithms and to develop the Binary Right Nulled Generalised LR algorithm - a new cubic worst case parser. We also compare the Right Nullable Generalised LR, Reduction Incorporated Generalised LR, Farshi, Tomita and Earley algorithms using the statistical data collected by PAT. Our study indicates that the overheads associated with some of the parsing algorithms may have significant consequences on their behaviour.