at least one of the set Si is a finite set

not more than one of the sets Si can be finite

at least one of the sets Si is an infinite set

not more than one of the sets Si can be infinite

Mathematical semantics

Interpretative semantics

Translational semantics

Axiomatic semantics

a* b*

(a | b)*

(ab)+

(a | b*)

without rewinding capability and unidirectional tape movement.

rewinding capacity, and unidirectional tape movement

without rewinding capability and bidirectional tape movement

rewinding capability and bidirectional tape movement

FSM can't remember arbitrarily large of information

FSM can't deterministically fix the mid-point

even if midpoint is known, FSM be can't be found whether, second half of the string matches the first half

all of these