Effective domain theory is applied to fuzzy logic to give suitable notions of semi-decidable and decidable L-subset. The connection with the notions of fuzzy Turing machines and fuzzy grammar given in literature is also investigated. This shows the inadequateness of these definitions and the difficulties in formulating an analogue of Church Thesis for fuzzy logic.

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...

A finite switchboard state machine is a specialized finite state machine. It is built by binding the concepts of switching state machines and commutative state machines. The main purpose of this paper is to give a specific algorithm for fuzzy finite switchboard state machine and also, investigates the concepts of switching relation, covering, restricted cascade products and wreath products of f...

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...

Traditionally the Turing Machine has been accepted as the universal model of computation. That is to say if a computation can be performed by any deterministic single processor computing machine, then it can be performed by a turing machine with at most a polynomial increase in running time. It has been suggested that traditional Turing Machines cannot efficiently simulate quantum mechanical ef...

We discuss combining physical experiments with machine computations and introduce a form of analogue-digital Turing machine. We examine in detail a case study where an experimental procedure based on Newtonian kinematics is combined with a class of Turing machines. Three forms of analogue-digital machine are studied, in which physical parameters can be set exactly and approximately. Using non-u...