The goal of this question is to give a simple proof that there are decision problems that admit no algorithm at all (independent of the runtime of the algorithm). = Define Σ as the set of all binary strings, i.e., Σ+ = {0, 1, 00, 01, 10, 11, 000, 001,...}. Observe that any decision problem II can be identified by a function fn: + → {0, 1}. Moreover, observe that any algorithm can be identified with a binary string in Σ. Use this to argue that "number" of algorithms is "much smaller" than "number" of decision problems and hence there should be some decision problems that cannot be solved by any algorithm.

The goal of this question is to give a simple proof that there are decision problems that admit no algorithm at all (independent of the runtime of the algorithm). = Define Σ as the set of all binary strings, i.e., Σ+ = {0, 1, 00, 01, 10, 11, 000, 001,...}. Observe that any decision problem II can be identified by a function fn: + → {0, 1}. Moreover, observe that any algorithm can be identified with a binary string in Σ. Use this to argue that "number" of algorithms is "much smaller" than "number" of decision problems and hence there should be some decision problems that cannot be solved by any algorithm.

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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