[sergiosgc]

A regex is a state machine. You can code the state machine by hand, but that does not invalidate the previous statement.

[mpax]

Depends on how you look at it.

Regex is a family of languages each of which can have various implementations. You could have a regex implementation that instead uses mutually recursive functions etc.

What is true is that regexes are typically not turing complete and can be represented with simple state machines.