Structural complexity of multi-valued partial functions computed by nondeterministic pushdown automata

This paper continues a systematic and comprehensive study on the structural properties of CFL functions, which are in general multivalued partial functions computed by one-way one-head nondeterministic pushdown automata equipped with write-only output tapes (or pushdown transducers), where CFL refers to a relevance to context-free languages. The CFL functions tend to behave quite differently from their corresponding context-free languages. We extensively discuss containments, separations, and refinements among various classes of functions obtained from the CFL functions by applying Boolean operations, functional composition, many-one relativization, and Turing relativization. In particular, Turing relativization helps construct a hierarchy over the class of CFL functions. We also analyze the computational complexity of optimization functions, which are to find optimal values of CFL functions, and discuss their relationships to the associated languages.