The Modelling of a Virtual Learning Environment can be accomplished through the modelling of states of a Turing Machine, where learning takes place through the transition of states in which knowledge products are built. In one state, a Turing Machine reads and as a result of this action may or may not write, and may or may not make a state transition. In the learning process modelled by states ...

¶2 · What is computable is anything that any Turing machine can compute, where the Turing machine was defined by Turing (1936). There are other definitions of computable, using for example Church’s λ-calculus, but all of them are mathematically equivalent. In any case, the term computable is defined with mathematical rigor. ¶3 · But, because what can be calculated was considered a vague notion,...

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 ...

A fuzzy linear programming approach is taken to solve an extended mathematical linear programming model to handle two important problems in cellular manufacturing systems simultaneously: Cell formation and layout design. We seek to minimize the total cost of inter-cell and intra-cell (forward and backward) movements and the cost of machines. The fuzzy demand and fuzzy machine capacity are also ...

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...

And-Parallel Machines* Nachum Dershowitz and Naomi Lindenstrauss Department of Computer Science, The Hebrew University, Jerusalem 91904, Israel The deterministic Turing machine, though abstract, can still be seen as a model of a realistic computer. The same cannot be said for the nondeterministic Turing machine as a model of parallel computing. We introduce several abstract machines with fine-g...

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...