I am learning automata theory. I think that there must be some relationship between state machine theory and dynamic programming. for the reason that the essence of dynamic programming is state transition equations. And automata theory is also deal with the problems about the transition between different states. Furthermore, since we can analysis string matching algorithms through the method using the state machine, I vaguely think that state machine can also help us understand DP more clearly.
However, I find there are few materials talking about this. I think that if we can apply automata theory to the process of learning dynamic programming techniques, it can help us understand so many DP problems which are usually too difficult and complex for us to understand.
Can anyone recommend some materials which are talking about the applications of automata theory in dynamic programming algorithms' designing or the analysis of DP problems using state machine theory?
ps. the terminology 'dynamic programming' here just refers to our normal understanding of that algorithm designing tricks, not that mathematics field which is created by Bellman.