Implicit characterizations of FPTIME and NC revisited

Various simplified or improved, and partly corrected well-known implicit characterizations of the complexity classes FPTIME and NC are presented. Primarily, the interest is in simplifying the required simulations of various recursion schemes in the corresponding (implicit) framework, and in developing those simulations in a more uniform way, based on a step-by-step comparison technique, thus consolidating groundwork in implicit computational complexity.