Can FSMs be Timed and Recursive?
Timed and recursive state machines are much more common than untimed state machines, at least among state machines that are deliberately designed as state machines rather than circuits designed by some other process that happen to also have the features of state machines. What makes you think these types aren't normally considered &quot;state machines&quot;?
Within the field of digital logic, if a circuit doesn't have recursion (aka feedback) and doesn't depend on time, then we usually call it &quot;combinatorial logic&quot; and consider it as not a state machine.