Complexity of Two-Dimensional Rank-Reducing Grammars

摘要

We study properties of a two-dimensional grammar introduced recently for use in document analysis and recognition. The grammar is obtained from the two-dimensional context-free grammar by restricting the form of productions. Variants (ranks) of the grammar with regard to productions complexity are defined. It is suggested that the lowest-rank variant can be considered as a natural generalization of the regular matrix grammar, which in addition has good properties with respect to the membership and emptiness problems. However, it is also showed that the higher-rank variants do not loosen complexity of the context-free grammar too much. There is a conditional lower bound preventing to propose a linear-time parsing algorithm. Moreover, the grammar is able to simulate the 2-counter Minsky machine, which results in non-recursive trade-offs and undecidability of the emptiness problem.