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. We will show the following. The internal deterministic Turing machines can do in ∗-polynomial time what a cla...

This paper presents Persistent Turing Machines (PTMs), a new way of interpreting Turing-machine computation, based on dynamic stream semantics. A PTM is a Turing machine that performs an in nite sequence of \normal" Turing machine computations, where each such computation starts when the PTM reads an input from its input tape and ends when the PTM produces an output on its output tape. The PTM ...

We show that, for any integer k, there is at least one language which is accepted by a k-tape real{time Turing machine, but cannot be accepted by a (k 1)-tape real{time Turing machine. We show therefore that the languages accepted by real{time Turing machines form an in nite hierarchy with respect to the number of tapes used.

The goal of getting computers to automatically solve problems is central to artificial intelligence, machine learning, and the broad area encompassed by what Turing called “machine intelligence” (Turing, 1948, 1950). In his talk entitled AI: Where It Has Been and Where It Is Going, machine learning pioneer Arthur Samuel stated the main goal of the fields of machine learning and artificial intel...

In this brief note, we give a simple information-theoretic proof that 2-state 3-symbol universal Turing machines cannot possibly exist, unless one loosens the definition of “universal”. Disclaimer: This article was authored by Craig Alan Feinstein in his private capacity. No official support or endorsement by the U.S. Government is intended or should be inferred. In May of 2007, Wolfram Researc...

We show that, for any integer k, there is at least one language which is accepted by a k-tape real{time Turing machine, but cannot be accepted by a (k ? 1)-tape real{time Turing machine. We show therefore that the languages accepted by real{time Turing machines form an innnite hierarchy with respect to the number of tapes used.

mere algorithm, formal system, computer, or robot. A few minutes of reading and pondering is a small price to pay for this distinction. Penrose presents a version of the theorem in which the true but unprovable sentence is an assertion that a certain computer program runs on forever. The technical formulation is in terms of an ideal computer known as a Turing machine. A Turing machine is a comp...

This paper presents the implementation of recursively enumerable language using Universal Turing machine for JFLAP platform. Automata play a major role in compiler design and parsing. The class of formal languages that work for the most complex problems belongs to the set of Recursively Enumerable Language (REL).RELs are accepted by the type of automata as Turing Machine. Turing Machines are th...

Problems in implementing DNA and other types of molecular computers stem from the inherent physical nature of molecules and their reactions. The current theory of computation makes assumptions that at best are very crude approximations of the physical chemistry. A theory which took into account the physical chemistry would likely be very diierent from what we have now and should help in designi...