A (finite non-deterministic) automaton is a quintuple M = (Q,Act,q0,F,T), where:
- Q is the set of states
- Act is the set of actions
- q0 is the starting state
- F is the set of final states
- T is the transition relation (T ⊆ Q × Act × Q)

Automata Behaviour: language equivalence
	(where L(M) is the set of all the sequences of input characters that bring the automaton M from its starting state to a final one)

>[!note] Language equivalence
>M1 and M2 are *language equivalent* if and only if L(M1)=L(M2)

![](../../Pasted%20image%2020250408091924.png)
By considering the starting states as also final, they both generate the same language, i.e.:
$$(20.(tea + 20.coffee))∗ = (20.tea + 20.20.coffee)∗$$


But, do they behave the same from the point of view of an external observer??
![](../../Pasted%20image%2020250408092853.png)
The essence of the difference is WHEN the decision to branch is taken
-  language equivalence gets rid of branching points
	- it is too coarse for our purposes!