Learning Equal Matrix Grammers and Multitape Automata with Structural Information

Equal matrix grammars are one of paralel rewriting systems. This type of parallel rewriting systems has been investigated in several areas such as L-systems and the syntactic pattern recognition. In this paper, we introduce two types of structural information and show that if these are available and there is a method of learning regular sets in polynomial time, then for any positive integer $k$ the class of equal matrix grammars of order $k$ is learnable in polynomial time. We also show that for any equal matrix language there exists an equal matrix grammar learnable efficiently only from positive structural examples. These results are applied to the problem of learning multitape automata and the same results are obtained.