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On Computability of Computable Problems

Asad Khaliq

TL;DR

This paper introduces new type of problems by constructing a transform technique and applying it on some computable problems so that the transformed problems can be computable of uncomputable.

Abstract

Computational problems are classified into computable and uncomputable problems. If there exists an effective procedure (algorithm) to compute a problem then the problem is computable otherwise it is uncomputable. Turing machines can execute any algorithm therefore every computable problem is Turing computable. Cardinality of Turing machines and computable problems is equal-both are countably infinite. In this paper we introduce new type of problems by constructing a transform technique and applying it on some computable problems. The transformed problems can be computable of uncomputable.

On Computability of Computable Problems

TL;DR

This paper introduces new type of problems by constructing a transform technique and applying it on some computable problems so that the transformed problems can be computable of uncomputable.

Abstract

Computational problems are classified into computable and uncomputable problems. If there exists an effective procedure (algorithm) to compute a problem then the problem is computable otherwise it is uncomputable. Turing machines can execute any algorithm therefore every computable problem is Turing computable. Cardinality of Turing machines and computable problems is equal-both are countably infinite. In this paper we introduce new type of problems by constructing a transform technique and applying it on some computable problems. The transformed problems can be computable of uncomputable.
Paper Structure (9 sections, 51 equations, 2 figures, 1 table)

This paper contains 9 sections, 51 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. Construction of Transform
  3. Stipulation machine
  4. Computation by a Turing machine $P_r$ and $P_r(t)$
  5. Examples of Transformed Problems
  6. Normalization of $f(Z,T)$ Transform
  7. Cardinality of $f(Z,T)$ Transformed Problems
  8. Mathematical Formulations of $f(Z,T)$ Transform
  9. Summary

Figures (2)

  • Figure 1: Flow of interactions between Turing machine and Stipulation machine
  • Figure 2: Normalization line of $f(Z,T)$ Transform