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...

The term recursively enumerable set has its roots in logic but today is most commonly seen in reference to the theory of Turing machines. The Turing machine model is conceptually a very simple one for an abstract computing device but has been proved to be so powerful that many believe that that which is “computable” or “recursive” in any reasonable sense of the word is computable by some Turing...

We formalise results from computability theory in the theorem prover Isabelle/HOL. Following the textbook by Boolos et al, we formalise Turing machines and relate them to abacus machines and recursive functions. We “tie the knot” between these three computational models by formalising a universal function and obtaining from it a universal Turing machine by our verified translation from recursiv...

In this paper we compare recursively enumerable subsets of R” in two computing models over real numbers: the Blum-Shub-Smale machine and the oracle Turing machine. We prove that any Turing RE open subset of RY is a BSS RE set, while a Turing RE closed set may not be a BSS RE set. As an application we show that the Julia set of any computable hyperbolic polynomial is decidable in the Turing comp...

From the point of view of a programmer, the robopsychology is a synonym for the activity is done by developers to implement their machine learning applications. This robopsychological approach raises some fundamental theoretical questions of machine learning. Our discussion of these questions is constrained to Turing machines. Alan Turing had given an algorithm (aka the Turing Machine) to descr...

In this article we describe a method of translation from a deterministic Turing machine to an extended mH splicing system. The accuracy of this translation is proved by a theorem which shows that the only string present in single copy is a coding of a connguration of the simulated Turing machine. A simpler translation from a universal Turing machine with three tapes to an extended mH system is ...

The different concepts involved in "reversal complexity"--counting reversals (sweeps), visits to a square, or crossing sequences--are discussed for nondeterministic off-line Turing machines with one working tape and for preset Turing machines, a generalization of two-way checking automata. Restriction to finite reversals or visits or crosses yields the same family, NSPACE(log2 n), for off-line ...

We describe a proof by a computer program of the Turing completeness of a computational paradigm akin to Pure LISP. That is, we define formally the notions of a Turing machine and of a version of Pure LISP and prove that anything that can be computed by a Turing machine can be computed by LISP. While this result is straightforward, we believe this is the first instance of a machine proving the ...