I don't believe TMs are considered FSMs (or FSAs :-). I have
always assumed that "FSM" referred to "deterministic finite
state automata" (DFAs) and their nondeterministic cousins.
It is easy to show that there are languages which are described
by Turing machines (& pushdown automata, an intermediate class of
machine), which are *not* describable by DFAs. One of the simplest
examples is the language of palindromes: strings which read the
same backwards and forwards. These are easily described by
push-down automata or Turing machines, but not by any DFA.
A Turing machine *does* have a finite-state component, but
it also has an unbounded stack, so the number of states that
the machine can be in is most definitely *not* finite.
Jeff
-- Jeff Adams Language Modeling Scientist Kurzweil Applied Intelligence http://www.kurz-ai.com/people/jeffa