This paper introduces a knowledge recognition algorithm (KRA) that is both a Turing machine algorithm and an Oracle Turing machine algorithm. By definition KRA is a non-deterministic language recognition algorithm. Simultaneously it can be implemented as a deterministic Turing machine algorithm. KRA applies mirrored perceptual-conceptual languages to learn member-class relations between the two...

Algorithms for computing on encrypted data promise to be a fundamental building block of cryptography. The way one models such algorithms has a crucial effect on the efficiency and usefulness of the resulting cryptographic schemes. As of today, almost all known schemes for fully homomorphic encryption, functional encryption, and garbling schemes work by modeling algorithms as circuits rather th...

Foundations of the notion of quantum Turing machines are investigated. According to Deutsch’s formulation, the time evolution of a quantum Turing machine is to be determined by the local transition function. In this paper, the local transition functions are characterized for fully general quantum Turing machines, including multi-tape quantum Turing machines, extending an earlier attempt due to ...

In this paper, we present a new way to simulate Turing machines using a specific form of Petri nets such that the resulting nets are capable of thoroughly describing behavior of the input Turing machines. We model every element of a Turing machine’s tuple F) q0, δ, Σ, b, Γ, Q, (i.e., with an equivalent translation in Colored Petri net’s set of elements with priority transitions such that the re...

After proposing the Turing Test, Alan Turing himself considered a number of objections to the idea that a machine might eventually pass it. One of the objections discussed by Turing was that no machine will ever pass the Turing Test because no machine will ever “have as much diversity of behaviour as a man”. He responded as follows: the “criticism that a machine cannot have much diversity of be...

Induction is a prevalent cognitive method in science, while inductive computations are popular in many fields of computer and network technology. The most advanced mathematical model of inductive computations and reasoning is an inductive Turing machine, which is natural extension of the most widespread model of computing devices and computations Turing machine. In comparison with Turing machin...

Since Richard Feynman introduced the notion of quantum computation in 1982, various models of \quantum computers" have been proposed. These models include quantum Turing machines and quantum circuits. In this paper we deene another quantum computational model, one-dimensional quantum cellular automata, and demonstrate that any quantum Turing machine can be eeciently simulated by a one-dimension...

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 ...

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,...