The Chemical Reaction Network model has been proposed as a programming language for molecular programming. Methods to implement arbitrary CRNs using DNA strand displacement circuits have been proposed, as have methods to prove the correctness of those or other implementations. However, the stochastic Chemical Reaction Network model is provably not deterministically Turing-universal, that is, it...

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...

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 ...

The strong, intermediate, and weak Turing impossibility properties are introduced. Some facts concerning Turing impossibility for stack machine programming are trivially adapted from previous work. Several intriguing questions are raised about the Turing impossibility properties concerning different method interfaces for stack machine programming.

For a long time it has been accepted that Turing machines are more powerful than generalized sequential machines. Since a generalized sequential machine is also a Turing machine, the class of Turing machines is at least as powerful as the class of generalized sequential machines. The purpose of this paper is to examine the adverb "more" from the aspect of work accomplished. Three manifestations...