The extension of deterministic cancellation parser to directly handle indirect and hidden left recursion

Traditional top-down parsers have both merits and constraints. Their structure is often simple and similar to the structure of the original grammar. Furthermore, they can handle empty rules but they cannot handle various types of left recursion in grammars. Transformation of left-recursive grammars during the normalization process will affect the semantic structure of the rules which is not appropriate. The bottom-up parsing methods, on the other hand, can easily handle left recursion while they are not capable of working with empty rules. The deterministic cancellation parser represented by the authors, which has a recursive-descent structure, can handle both empty rules and direct left recursion by combining top-down and bottom-up cycles during the construction of the parse tree. In fact, it employs a non-canonical approach in the parsing process. The most important struggle in this paper is to extend the original parser´s ability to handle all kinds of left recursion, including indirect and hidden left recursion, which are more complicated to be handled. The resulting parser is a deterministic cancellation parser with a recursive decent structure, which has more acceptance power, because of its capability of working with all kinds of left recursion without any need for transforming them into non left-recursive equivalents.