The equivalence of nondeterministic and deterministic Turing machines was noticed in Evey (1963). The undecidability of the membership problem for Turing machines is due to Turing (1936). Chomsky (1959) showed that the class of languages that Turing machines accept is the Type 0 languages.
Myhill (1960) identified the deterministic linear bounded automata. Chomsky (1959) introduced the context-sensitive grammars. Kuroda (1964) introduced the Type 1 grammars and the nondeterministic linear bounded automata, and showed their equivalency to the class of context-sensitive grammars. Landweber (1963) showed that there are languages that cannot be accepted by any deterministic linear bounded automaton but that can be accepted by a linear bounded automaton.
Post (1946) showed that PCP is an undecidable problem. The undecidability of the equivalence problem for finite-state transducers is due to Griffiths (1968). The undecidability of the equivalence problem for context-free languages, and the undecidability of the problem of determining for any given context-free language whether it is regular, are due to Bar-Hillel , Perles , and Shamir (1961). The undecidability of the ambiguity problem for context-free languages is due to Chomsky and Schutzenberger (1963).
Further coverage for the above topics can be found in Hopcroft and Ullman (1979).