Serial Composition of 2-Way Finite-State Transducers and Simple Programs on Strings

Hopcroft and Ullman ~i] described an algorithm for reverse run of deterministic generalized sequential machines. This algorithm does not go beyond abilities of 2-way finite automata. The algorithm was then used [ 2 ] in the proof of the fact that serial composition of a deterministic gsm A 1 and a 2way deterministic finite-state transducer A 2 can be replaced by a single 2-way deterministic finite-state transducer, say A 3. Let us recall the main idea of the proof (c.f. fig. i).