Abstract : In this research paper, I will give you an abstract level of familiarization with Hyper Computation. In my work, I will give you an introduction about hyper computation and then relate the hyper computation with turing machine. Later in this research paper, we analyze different hyper machines and some resources which are very essential in developing a hyper computing machine, and then see some implications of hyper computation in the field of computer science. Introduction (Hyper Computation): The turing machine was developed for computation. Alan turing introduced the imaginary machine to the world, which could take input (these inputs usually represents the various mathematical objects), and then produces some output after …show more content…
We3 can construct a machine M` that takes input I and representation of a turing machine M. now if we examine the simulation of this machine , we come to know that if M doesn’t halt then M` also not halt. Similarly if M halts, M` also halts, but instead of computing the result of M on I it outputs the number I. Thus we can say that M` computes the halting function correctly if value of function is 1 and it diverges otherwise. It is now can be said that M` semi computes the halting …show more content…
By theoretical meanings theses hyper machines are just like turing machines, using abstract resources to manipulate or compute abstract objects including symbols and numbers. Therefore when someone claims that there exist a machine for a halting problem, then it means there is a theoretical machine exist instead of physical one. However the hyper computational resources are often physically praised and there is interest whether these machines are physically exist or not in theoretical way as well as in practice. Now I will represent the different models of hyper computing machines and presents resources that these machines used. Mine focus will be on mathematical nature of these resources. 1. O-Machines It is considered as a turing machine which is equipped with an oracle , making it capable to answer such questions about the membership of specific set of natural numbers. This machine also equipped with three special states which are the 1-state, 0-state and call state along with a special marker symbol ᶙ. This machine first writes ᶙ on its two squares of the tape and then enter the call state. This procedure sends up a query to to the oracle. If the number of tape squares between the ᶙ symbol is an element of oracle set then this machine ends up in 1-state otherwise ends up in
Andy Clark strongly argues for the theory that computers have the potential for being intelligent beings in his work “Mindware: Meat Machines.” The support Clark uses to defend his claims states the similar comparison of humans and machines using an array of symbols to perform functions. The main argument of his work can be interpreted as follows:
ABSTRACT: I examine some recent controversies involving the possibility of mechanical simulation of mathematical intuition. The first part is concerned with a presentation of the Lucas-Penrose position and recapitulates some basic logical conceptual machinery (Gödel's proof, Hilbert's Tenth Problem and Turing's Halting Problem). The second part is devoted to a presentation of the main outlines of Complexity Theory as well as to the introduction of Bremermann's notion of transcomputability and fundamental limit. The third part attempts to draw a connection/relationship between Complexity Theory and undecidability focusing on a new revised version of the Lucas-Penrose position in light of physical a priori limitations of computing machines. Finally, the last part derives some epistemological/philosophical implications of the relationship between Gödel's incompleteness theorem and Complexity Theory for the mind/brain problem in Artificial Intelligence and discusses the compatibility of functionalism with a materialist theory of the mind.
The Turing test was a test that allows humans to evaluate the question “can machines think?” Turing evaluates that one should not ask if machines can think, but conduct an experiment which can prove that it can think. In order to answer this question, Turing created
If a machine passes the test, then it is clear that for many ordinary people it would be a sufficient reason to say that that is a thinking machine. And, in fact, since it is able to conversate with a human and to actually fool him and convince him that the machine is human, this would seem t...
This essay will consist in an exposition and criticism of the Verification Principle, as expounded by A.J. Ayer in his book Language, Truth and Logic. Ayer, wrote this book in 1936, but also wrote a new introduction to the second edition ten years later. The latter amounted to a revision of his earlier theses on the principle.It is to both accounts that this essay shall be referring.
Turing earned a fellowship at King’s college and the following year the Smith’s Prize for his work in probability theory. Afterward, he chose a path away from pure math into mathematical logic and began to work on solving the Entscheidungsproblem, a problem in decidability. This was an attempt to prove that there was a method by which any given mathematical assertion was provable. As he began to dive in to this he worked on first defining what a method was. In doing so he began what today is called the Turing Machine. The Turing Machine is a three-fold inspiration composed of logical instructions, the action of the mind, and a machine which can in principle be embodied in a practical physical form. It is the application of an algorithm embodied in a finite state machine.
Created by English mathematician Alan Turing, the Turing test (formerly known as the imitation game) is a behavioral approach that assesses a system’s ability to think. In doing so, it can determine whether or not that system is intelligent. This experiment initiated what is now commonly known as artificial intelligence.
There are many different beginnings to the origins of computers. Their origins could be dated back more than two thousand years ago, depending on what a person means when they ask where the first computer came from. Most primitive computers were created for the purpose of running simple programs at best. (Daves Old Computers) However, the first ‘digital’ computer was created for the purposes of binary arithmetic, otherwise known as simple math. It was also created for regenerative memory, parallel processing, and separation of memory and computing functions. Built by John Vincent Atanasoff and Clifford Berry during 1937-1942, it was dubbed the Atanasoff Berry Computer (ABC).
Although the majority of people cannot imagine life without computers, they owe their gratitude toward an algorithm machine developed seventy to eighty years ago. Although the enormous size and primitive form of the object might appear completely unrelated to modern technology, its importance cannot be over-stated. Not only did the Turing Machine help the Allies win World War II, but it also laid the foundation for all computers that are in use today. The machine also helped its creator, Alan Turing, to design more advanced devices that still cause discussion and controversy today. The Turing Machine serves as a testament to the ingenuity of its creator, the potential of technology, and the glory of innovation.
Computer engineering started about 5,000 years ago in China when they invented the abacus. The abacus is a manual calculator in which you move beads back and forth on rods to add or subtract. Other inventors of simple computers include Blaise Pascal who came up with the arithmetic machine for his father’s work. Also Charles Babbage produced the Analytical Engine, which combined math calculations from one problem and applied it to solve other complex problems. The Analytical Engine is similar to today’s computers.
Ceruzzi, P. E. (1998). A history of modern computing (pp. 270-272). London, England: The MIT Press.
In the past few decades, one field of engineering in particular has stood out in terms of development and commercialisation; and that is electronics and computation. In 1965, when Moore’s Law was first established (Gordon E. Moore, 1965: "Cramming more components onto integrated circuits"), it was stated that the number of transistors (an electronic component according to which the processing and memory capabilities of a microchip is measured) would double every 2 years. This prediction held true even when man ushered in the new millennium. We have gone from computers that could perform one calculation in one second to a super-computer (the one at Oak Ridge National Lab) that can perform 1 quadrillion (1015) mathematical calculations per second. Thus, it is only obvious that this field would also have s...
Von Neumann architecture, or the Von Neumann model, stems from a 1945 computer architecture description by the physicist, mathematician, and polymath John von Neumann and others. This describes a design architecture for an electronic digital computer with a control unit containing an instruction register and program counter , external mass storage, subdivisions of a processing unit consisting of arithmetic logic unit and processor registers, a memory to store both data and commands, also an input and output mechanisms. The meaning of the term has grown to mean a stored-program computer in which a command fetch and a data operation cannot occur at the same time because they share a common bus. This is commonly referred to as the Von Neumann bottleneck and often limits the performance of a system.
Artificial intelligence is a concept that has been around for many years. The ancient Greeks had tales of robots, and the Chinese and Egyptian engineers made automations. However, the idea of actually trying to create a machine to perform useful reasoning could have begun with Ramon Llull in 1300 CE. After this came Gottfried Leibniz with his Calculus ratiocinator who extended the idea of the calculating machine. It was made to execute operations on ideas rather than numbers. The study of mathematical logic brought the world to Alan Turing’s theory of computation. In that, Alan stated that a machine, by changing between symbols such as “0” and “1” would be able to imitate any possible act of mathematical
The history of the computer dates back all the way to the prehistoric times. The first step towards the development of the computer, the abacus, was developed in Babylonia in 500 B.C. and functioned as a simple counting tool. It was not until thousands of years later that the first calculator was produced. In 1623, the first mechanical calculator was invented by Wilhelm Schikard, the “Calculating Clock,” as it was often referred to as, “performed it’s operations by wheels, which worked similar to a car’s odometer” (Evolution, 1). Still, there had not yet been anything invented that could even be characterized as a computer. Finally, in 1625 the slide rule was created becoming “the first analog computer of the modern ages” (Evolution, 1). One of the biggest breakthroughs came from by Blaise Pascal in 1642, who invented a mechanical calculator whose main function was adding and subtracting numbers. Years later, Gottfried Leibnez improved Pascal’s model by allowing it to also perform such operations as multiplying, dividing, taking the square root.