Models of Computation Lecture : Turing Machines [fa''']

Although Turing did not know it at the time, he was not the first to prove that the Entscheidungsproblem had no algorithmic solution. The first such proof is implicit in the work of Kurt Gödel; in lectures on his incompleteness theorems2 at Princeton in 1934, Gödel described a model of general recursive functions, which he largely credited to Jacques Herbrand.3 Gödel’s incompleteness theorem can be viewed as a proof that some propositions cannot be proved using general recursive functions. However, Gödel viewed his definition as a “heuristic principle” rather than an accurate model of effective computation, or even a complete definition of recursion. The first published proof was written by Alonzo Church and published just a new months before Turing’s paper, using another different model of computation, now called the untyped λ-calculus. Turing and Church developed their results independently; indeed, Turing rushed