We derive results of the following flavor:
If a combinatorial optimization problem can be formulated via a dynamic
program of a certain structure and if the involved cost and transition
functions satisfy certain arithmetical and structural conditions, then
the optimization problem automatically possesses a fully polynomial time
approximation scheme (FPTAS).

Our characterizations provide a natural and uniform approach to fully
polynomial time approximation schemes.
We illustrate their strength and generality by deducing from them the
existence of FPTASs for a multitude of scheduling problems.
Many known approximability results follow as corollaries from
our main result.