Abstract

We introduce oracle Turing machines with neutrosophic values allowed in the oracle information and then give some results when one is permitted to use neutrosophic sets and logic in relative computation. We also introduce a method to enumerate the elements of a neutrosophic subset of natural numbers.

Highlights

  • In classical computability theory, algorithmic computation is modeled by Turing machines, which were introduced by Alan M

  • We introduced the neutrosophic counterpart of oracle Turing machines with neutrosophic values allowed in the oracle tape

  • For this we presented a new type of oracle tape where each cell contains a triplet of three probability values, namely for the membership, non-membership, and indeterminacy

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Summary

Introduction

Algorithmic computation is modeled by Turing machines, which were introduced by Alan M. We shall not delve into the details about what is meant by a function or set that is computable by a Turing machine. For a given an oracle Turing machine with the characteristic sequence of a set S provided in the oracle tape, functions are denoted as computable by the machine relative to the oracle S. If n were a natural number and if A were a neutrosophic set, there would be a probability distribution p∈ (n) + p6∈ (n) + p I (n) = 1, where p∈ (n) denotes the probability of n being a member of A, p6∈ (n) denotes the probability of n not being a member of A, and p I (n) denotes the degree of probability that the membership of n is indeterminate in A. Any neutrosophic subset A of natural numbers (we shall occasionally denote such a set by A N ) is defined in the form of ordered triplets:.

Oracle Turing Machines with Neutrosophic Values
Neutrosophic Enumeration and Criterion Functions
Conclusions
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