Modern computability theory began with Turing [Turing, 1936], where he introduced the notion of a function computable by a Turing machine. Soon after, it was shown that this definition was equivalent to several others that had been proposed previously and the Church-Turing thesis that Turing computability captured precisely the informal notion of computability was commonly accepted. This isolat...

• Every computation can be viewed as a graph that satisfies monadic second-order formula. recursively enumerable relation computed by such For this notion of computability, graphs need not coded strings or numbers. A binary on is if and only it formula logic. The latter means the defines set graphs, in usual way, each “computation graph” determines pair consisting an input output graph.