I assume that most students have encountered Turing machines before. (Students who have not may want to look at Sipser’s book [3].) A Turing machine is defined by an integer k ≥ 1, a finite set of states Q, an alphabet Γ, and a transition function δ : Q×Γk → Q×Γk−1×{L, S,R}k where: • k is the number of (infinite, one-dimensional) tapes used by the machine. In the general case we have k ≥ 3 and ...

In this paper we explore deep learning models with memory component or attention mechanism for question answering task. We combine and compare three models, Neural Machine Translation [1], Neural Turing Machine [5], and Memory Networks [15] for a simulated QA data set [14]. This paper is the first one that uses Neural Machine Translation and Neural Turing Machines for solving QA tasks. Our resu...

The present paper proves that P = NP. The proof, presented in this paper, is a constructive one: The program of a polynomial time deterministic multi-tape Turing machine M ∃AcceptingP ath, which determines if there exists an accepting computation path of a polynomial time non-deterministic single-tape Turing machine M

A computable real function F on [0,1] is constructed such that there exists an exponential time algorithm for the evaluation of the function on [0,1] on Turing machine but there does not exist any polynomial time algorithm for the evaluation of the function on [0,1] on Turing machine (moreover, it holds for any rational point on (0,1))

This is a review of three, agent control algorithm, replication experiments. In the 1948 essay, Intelligent Machinery, the English mathematician Alan Turing described an algorithm for constructing a machine that he claimed was capable of cybernetic (or steered feedback) self-organization. There are few, if any, references in either the historical or the technical literatures to instantiations m...

It is reasonable to assume that quantum computations take place under the control of the classical world. For modeling this standard situation, we introduce a Classically-controlled Quantum Turing Machine (CQTM) which is a Turing machine with a quantum tape for acting on quantum data, and a classical transition function for a formalized classical control. In CQTM, unitary transformations and qu...

We enhance the notion of a computation of the classical theory of computing with the notion of interaction. In this way, we enhance a Turing machine as a model of computation to a Reactive Turing Machine that is an abstract model of a computer as it is used nowadays, always interacting with the user and the world.

: From the physico-mathematical view point, the imitation game between man and machine, proposed by Turing in 1950, is a game between a discrete and a continuous system. Turing stresses several times the laplacian nature of his discrete-state machine, yet he tries to show the undetectability of a functional imitation, by his machine, of a system (the brain) that, in his words, is not a discrete...

Ohya and Volovich have proposed a new quantum computation model with chaotic amplification to solve the SAT problem, which went beyond usual quantum algorithm. In this paper, we generalize quantum Turing machine, and we show in this general quantum Turing machine (GQTM) that we can treat the Ohya-Volovich (OV) SAT algorithm.

This paper describes the simulation of an S(n) spacebounded deterministic Turing machine by a reversible Turing machine operating in space S(n). It thus answers a question posed by Bennett in 1989 and refutes the conjecture, made by Li and Vitanyi in 1996, that any reversible simulation of an irreversible computation must obey Bennett’s reversible pebble game rules.