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.

Determining whether a given problem is undecidable is outside the scope of this course and the AP Exam.

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.