# 3.18 Undecidable Problems

## Enduring Understanding

There exist problems that computers cannot solve, and even when a computer can solve a problem, it may not be able to do so in a reasonable amount of time.

## Learning Objective

Explain the existence of undecidable problems in computer science.

## Essential Knowledge

A decidable problem is a decision problem for which an algorithm can be written to produce a correct output for all inputs (e.g., “Is the number even?”).

An undecidable problem is one for which no algorithm can be constructed that is always capable of providing a correct yes-or-no answer.

{% hint style="info" %}
Determining whether a given problem is undecidable is outside the scope of this course and the AP Exam.
{% endhint %}

An undecidable problem may have some instances that have an algorithmic solution, but there is no algorithmic solution that could solve all instances of the problem.


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