2017 Volume 60 Issue 2 Pages 136-155
This paper studies the relation between a given nondeterministic discrete decision process (nd-ddp) and a nondeterministic sequential decision process (nd-sdp), which is a finite nondeterministic automaton with a cost function, and its subclasses (nd-msdp, nd-pmsdp, nd-smsdp). We show super-strong representation theorems for nd-sdp and its subclasses, for which the functional equations of nondeterministic dynamic programming are obtainable. The super-strong representation theorems provide necessary and sufficient conditions for the existence of the nd-sdp and its subclasses with the same set of feasible policies and the same cost value for every feasible policy as the given process nd-ddp.
