Relations and Transductions Realized by Restarting Automata

In the present thesis we introduce several ways of extending restarting automata to devices for realizing binary (word) relations, which is mainly motivated by linguistics. In particular, we adapt the notion of input/output-relations and proper-relations to restarting automata and to parallel communicating systems of two restarting automata (PC-systems). Further, we introduce a new model, called restarting transducer. Concerning input/outputand proper-relations we show equivalences of relation classes de ned by restarting automata to the well-known classes of rational relations and pushdown relations. Further, regarding the proper-relations realized by certain PC-systems of two restarting automata, we show that this class includes all computable relations. The main part of this work concerns restarting transducers. A restarting transducer is a restarting automaton equipped with an output function. In this way we show that the hierarchy of language classes de ned by restarting automata can be partly transfered to a corresponding hierarchy of relation classes. Moreover, by using results from the concepts introduced before, we prove that monotone types of restarting transducers de ne a hierachy of relation classes within the length-bounded pushdown relations. We conclude this thesis by establishing an upper bound and a di erent point of view on relations realized by restarting transducers through the concept of Transducing by Observing.