Implications Of Hyper Computation

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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

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