Machine intelligence dates back to 1936, when Alan Turing proposed the idea of a universal mathematics machine, a theoretical concept in the mathematical theory of computability. Turing and Emil Post independently proved that determining the decidability of mathematical propositions is equivalent to asking what sort of sequences of a finite number of symbols can be recognized by an abstract mac...

The benchmark for computation is typically given as Turing computability; the ability for a computation to be performed by a Turing Machine. Many languages exploit (indirect) encodings of Turing Machines to demonstrate their ability to support arbitrary computation. However, these encodings are usually by simulating the entire Turing Machine within the language, or by encoding a language that d...

In this note I would like to confront some conventional concepts of information processing (selective dissipation) with the facts of molecular biophysics. There are a number of theoretical computers which provide formalizations of the intuitive notion of effective (or algorithmic) information processing. The best known of these is the Turing machine. This is a finite automaton along with a memo...

We outline a theory of evolutionary computation using a formal model of evolutionary computation--the Evolutionary Turing Machine--which is introduced as the extension of the Turing Machine model. Evolutionary Turing Machines provide a better and a more complete model for evolutionary computing than conventional Turing Machines, algorithms, and Markov chains. The convergence and convergence rat...

The Turing machine is studied with new methods motivated by the notion of recurrence in classical dynamical systems theory. The state cycle of a Turing machine is introduced. It is proven that each consecutive repeating state cycle in a Turing machine determines a unique periodic configuration (point) and vice versa. This characterization is a periodic point theorem for Turing machines. A Turin...

So far we have talked about quantum computations involving only a few qubits. In this lecture I'd like to begin to discuss how we might scale this up to more than a few qubits and to make something resembling a valid model of computation. To do proper justice to this task, we should probably review the history of the classical theory of computation, and the struggles which the early pioneers in...

The Turing Machine was designed by Alan Turing to serve as a general computational model. The machine has a tape to which data can be written by a head. A tape consists of cells where each cell has a value (similar to a cell on a hard-drive, albeit the cells of a Turing Machine’s tape can have more than two states) and that value can be changed by the head. The head can also be in multiple stat...

In Turing (1937) a characterization is given of those functions that can be computed using a mechanical device. Moreover it was shown that some precisely stated problems cannot be decided by such functions. In order to give evidence for the power of this model of computation, Turing showed in the same paper that machine computability has the same strength as definability via λ-calculus, introdu...