Parsing 2-dimensional language

2-Dimensional Context-Free Grammar (2D-CFG) for 2-dimensional input text is introduced and efficient parsing algorithms for 2D-CFG are presented. In 2D-CFG, a grammar rule's right hand side symbols can be placed not only horizontally but also vertically. Terminal symbols in a 2-dimensional input text are combined to form a rectangular region, and regions are combined to form a larger region using a 2-dimensional phrase structure rule. The parsing algorithms presented in this paper are the 2D-Ear1ey algorithm and 2D-LR algorithm, which are 2-dimensionally extended versions of Earley's algorithm and the LR(O) algorithm, respectively.