I understand that DFAs recognize regular languages, and PDAs context-free languages, but these are a little bit too theoretical. I am wondering if we can implement common functions or solve common problems with DFAs and PDAs instead of Turing machines (or in a Turing-complete language).
By "common", I mean either one of the following:
- problems like those in algorithm analysis and data structures, i.e. sorting, shortest path, etc.
- functions seen in the everyday work of a common programmer, probably some useful business logic.