Parallel parsing of context-free text-structure grammars

We introduce a new class of grammars, called text-structure grammars, for representing and generating texts where texts are viewed as two-dimensional objects. We investigate the complexity of parsing texts generated by context-free text-structure grammars. We show that the sequential time complexity of parsing a text of size n×n is O(n⁴). The space complexity of this sequential parsing is O(n ³). Using parallel random access machines (i.e. PRAM), we show that parsing texts can be done in O(log²(n)) or in O(nlog²(n)) time. Using array machines, we prove that this problem can be solved in O(n³) time in one dimensional array machine and in O(n²) (resp. O(n))in two-dimensional (resp. three dimensional) array machines