I think the insight is that each formalism is defined by/equivalent to the input language that it is able to parse; State machines can do regular expressions,

I think the insight is that each formalism is defined by/equivalent to the input language that it is able to parse; State machines can do regular expressions, but they can't parse matching brackets, Stack machines can do BNF grammars - but they don't have counters; also Stack machines are more general than state machines; each regular expression can be expressed by an equivalent BNF grammar. Turing machines can parse Perl - that means any language that depends on the context; this is because Turing machines have counters/memory. Also Turing machines are more general than stack machines; each BNF grammar can also be parsed by a Turing machine. All this business of deterministic/non deterministic machines is about efficiency of the parser; nice to know.