Does Thompson's algorithm produce optimal NFAs?

I'm using Thompson's algorithm to convert from a regular expression to a NFA. Is Thompson's algorithm guaranteed to always output a minimal NFA, i.e., a NFA with the smallest possible number of states?

For instance, consider this example. I have the regular expression $(a|b)$. According to this website, Thompson's algorithm converts it to the following NFA:

o--->o
  /ε  a  \ε
>o        O
  \ε  b  /ε 
   o--->o

However, the following NFA is smaller and seems like it would also be equivalent:

o
 a/ \ε
>o   O
 b\ /ε 
   o

Why doesn't Thompson's algorithm output the latter NFA? What did I miss here? Is that Thompson's construction algorithm not optimized at all?

Minimizing NFAs is known to be PSPACE-hard: Meyer and Stockmeyer showed that given an NFA, it is PSPACE-hard to find the size of the minimal equivalent NFA, and Jiang and Ravikumar showed that given a DFA, finding the size of the minimal equivalent NFA is PSPACE-hard. Later some hardness of approximation results were proved, showing that it is even hard to approximate the size of the minimal equivalent NFA. See these lecture notes by Artem Kaznatcheev for more details.

Since a regular expression can be converted to an NFA of comparable size using Thompson's algorithm, these hardness results show that we can't expect any efficient algorithm to convert an regular expression to a minimal-size NFA.

StackExchange Computer Science Q#43845, answer score: 11