Branching Tree Grammars in TREEBAG

In this master thesis project a class of tree grammars called “Branching tree grammar” has been implemented into the TREEBAG system. A tree grammar is a device that generates a language of mathematical trees, according to rules specified by the user. These trees can then be transformed into for example pictures, by other components in TREEBAG. The branching tree grammar, which is a class of grammars known from literature, can generate more advanced languages than the grammars previously implemented in TREEBAG. The implementation uses an approach of analyzing the branching tree grammar, and replacing it with a series of simpler components, namely regular tree grammars and top-down tree transducers. These components, when used together in a sequence transforming each others’ output, will generate exactly the same language as the specified branching tree grammar. Regular tree grammars and top-down tree transducers were already implemented in TREEBAG. Therefore the core implementation of branching tree grammar consists of an algorithm that reads a file that specifies a branching tree grammar, translates it into the equivalent series of simpler components, and outputs files describing regular tree grammars and top-down tree transducers. These files are then processed by the existing TREEBAG-components. As a basis for the translation an algorithm has been used, which was taken from a constructive proof, in which it was proved that for each branching tree grammar, there exists a sequence of a regular tree grammar and top-down tree transducers, which generates the same language. However, in order to get an implementation that obeys feasible time requirements, and which is also fairly easy to use, the given algorithm to obtain the regular tree grammar and transducers had to be heavily reconstructed. This report describes at a relatively formal level the given translation algorithm as well as several improved versions of the algorithm. The advantages of the different algorithms are discussed, and some proofs and proof sketches for the correctness of the improved algorithms are also included.