What is the difference between finite automata and Büchi automata? as the title suggests, I was struggling to define the differences between finite and Büchi automata and how they are represented. 



From an assignment I'm working on, this automaton can be depicted as both infinite automaton and Büchi automaton.

Can you give me an example for each of those automatons to understand the differences?
There is no difference in the specification (syntax). The only difference is in the interpretation (semantics). The language accepted by a DFA consists of finite strings defined in a certain way given the DFA, and the language accepted by the corresponding B&uuml;chi automaton consists of infinite strings defined in a certain way.

Indeed, you can leverage this connection to prove results such as:


  An $\omega$-language is recognizable by a deterministic Büchi automaton iff it is the limit language of some regular language.


For a proof, see Wikipedia.