I've been revising Theory of Computation for fun and this question has been nagging me for a while (funny never thought of it when I learnt Automata Theory in my undergrad). So "why" exactly do we study deterministic and non-deterministic finite automata (DFA/NFAs)? So here are some answers I came up with after soliloquing but still fail to see their overall contribution to the 'aha' moment:
- To study what they are and aren't capable of i.e. limitations
- Since they are the basic models of theoretical computation and would lay the foundation of other more capable models of computation.
- What makes them 'basic'? Is it that they have only one bit of storage and state transitions?
- Okay, so what? How does all this contribute to answer the question of computability? It seems Turing machines help understand this really well and there are 'lesser' models of computations like PDAs, DFA/NFAs/Regexes etc. But if one didn't know FAs what is it that they are missing out on?
So although I 'get it' to some extent, I am unable to answer this question to myself? How best would you explain 'why study D/N-FAs'? What's the question they seek to answer? How does it help and why is it the first thing taught in Automata Theory?
PS: I'm aware of the various lexicographic applications and pattern matchers that can be implemented as such. However, I don't wish to know what it can be used for practically but what was their reason for use/invention/design during the culmination of studying the theory of computation. Historically speaking what led one to start with this and what 'aha' understanding is it supposed to lead to? If you were to explain their importance to CS students just beginning to study Automata Theory, how'd you do it?