Other Formalisms

Abstract

In this lecture and the next we take a brief look at some of the other traditional formalisms that are computationally equivalent to Turing machines. Each one of these formalisms embodies a notion of computation in one form or another, and each can simulate the others. In addition to Turing machines, we’ll consider

• Post systems;

• type 0 grammars;

• μ-recursive functions (μ = “mu”, Greek for m);

• λ-calculus (λ = “lambda”, Greek for 1);

• combinatory logic; and

• while programs.