enters an accept state, or 2) an undefined transition is encountered. In the latter case, the string is rejected, by definition. Definition 1 A Turing machine (TM) is formally specified by the 7-tuple (\Sigma; \Gamma; Q; q 0 ; b; A; \Delta), where 1. \Sigma is a finite non-empty set called the input

New research results from computer science, physics, logics, cognitive science, bioinformatics and related research fields provide strong reasons for us to try to generalize the idea of computing. Generalization of Turing concept of computation in essentially two ways: 1. Generalization

Notice: This PDF version was distributed by request to members of the Friends of the SEP Society and by courtesy to SEP content contributors. It is solely for their fair use. Unauthorized distribution is prohibited. To learn how to join the Friends of the SEP Society and obtain authorized PDF versions of SEP entries, please visit

Abstract. Accelerating Turing machines are Turing machines of a sort able to perform tasks that are commonly regarded as impossible for Turing machines. For example, they can determine whether or not the decimal representation of π contains n consecutive 7s, for any n; solve the Turing-machine

Comparative tests work by finding the difference (or the absence of difference) between a reference subject and an evaluee. The Turing Test, in its standard interpretation, takes (a subset of) the human species as a reference. Motivated by recent findings and developments in the area of machine

Abstract. Using nonstandard analysis, we will extend the classical Turing machines into the internal Turing machines. The internal Turing machines have the capability to work with infinite (∗-finite) number of bits while keeping the finite combinatoric structures of the classical Turing machines

In this paper we describe and analyze models of problem solving and computation going beyond Turing Machines. Three principles of extending the Turing Machine's expressiveness are identified, namely, by interaction, evolution and infinity. Several models utilizing the above principles

Abstract-Now-a-days every computing device is based on the Turing Machine. It is known that classical physics is sufficient to explain macroscopic phenomena, but is not to explain microscopic phenomena like the interference of electrons. In these days, speed-up and down-sizing of computing devices

In this project we look at Turing Machines and how they are used to prove properties about various problems. We examine the concept of multiple tape Turing Machines and how they relate to nondeterministic Turing Machines. We pay special attention to Minsky's Theorem which states that a Turing

Abstract. Turing machines exposed to a small stochastic noise are considered. An exact characterisation of their ( ≈ Π 0 2) computational power (as noise level tends to 0) is obtained. From a probabilistic standpoint this is a theory of large deviations for Turing machines. 1