Closure under union and composition of iterated rational transductions

We proceed our work on iterated transductions by studying the closure under union and composition of some classes of iterated functions. We analyze this closure for the classes of length-preserving rational functions, length-preserving subsequential functions and length-preserving sequential functions with terminal states. All the classes we obtain are equal. We also study the connection with deterministic context-sensitive languages. AMS Subject Classification. 68Q45; 68Q42, 68Q70.