Using Linear Positional Grammars for the LR Parsing of 2-D Symbolic Languages

In this paper we present a grammar formalism for the generation and parsing of two-dimensional symbolic languages. Linear Positional Grammars (or LPGs for short) are an immediate generalization of the context-free string grammars. Through the use of general spatial relations they allow the definition of pictures whose symbols span on a two-dimensional space. Due to their analogy to context-free string grammars, LPGs can be used to construct an LR-based parser which uses the spatial relations to navigate the input. We study ambiguous grammars and present several ways to solve them. Moreover we provide an algorithm to translate a linear positional grammar into a contextfree grammar with actions and suggest a general methodology to parse twodimensional symbolic languages by making use of the well-known tool YACC (Yet Another Compiler-Compiler [25]). As an example, we construct a parser for a subset of the two-dimensional arithmetical expression language.