Deterministic context free languages can be recognized by a deterministic Turing machine in polynomial time.
Lower elementary recursive functions are limited to polynomial time growth.
From this is it correct to derive that deterministic push down automata are of equal power to the lower elementary recursive functions?
Edit: My reasoning is that because the deterministic context free languages can be recognized in polynomial time that a deterministic push down automata is implementing a boolean function of up to that complexity. The lower elementary functions are also up to polynomial time. As such are they not equal in power?