What is the enlightenment I'm supposed to attain after studying finite automata?

Abstraction: Purpose of finite automata in theory of computation curriculum

Key points:

• DFAs and NFAs are the simplest models of computation: single-bit storage with deterministic or nondeterministic state transitions
• Studying FA reveals limitations of computation, laying groundwork for the Chomsky hierarchy (FA < PDA < TM)
• The key insight is understanding what classes of problems a model cannot solve, not merely what it can
• FA are the formal foundation for regular expressions, lexers, and pattern matchers used in practice
• Progression DFA/NFA -> PDA -> Turing machine frames the central computability question: what is computable at all?

Connections: Finite Automata · Theory Of Computation · Formal Languages · Computational Complexity

Source: http://cstheory.stackexchange.com/questions/14811/what-is-the-enlightenment-im-supposed-to-attain-after-studying-finite-automata