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Computer Science Principles
  • Introduction
  • Overview
  • Course at a Glance
  • Course Exam Description
  • Create Performance Task
  • Reference Sheet
  • Resources
  • Big Idea 1
    • 1.1 Collaboration
    • 1.2 Program Function and Purpose
    • 1.3 Program Design and Development
    • 1.4 Identifying and Correcting Errors
  • Big Idea 2
    • 2.1 Binary Numbers
    • 2.2 Data Compression
    • 2.3 Extracting Information from Data
    • 2.4 Using Programs with Data
  • Big Idea 3
    • 3.1 Variables and Assignments
    • 3.2 Data Abstraction
    • 3.3 Mathematical Expressions
    • 3.4 Strings
    • 3.5 Boolean Expression
    • 3.6 Conditionals
    • 3.7 Nested Conditionals
    • 3.8 Iteration
    • 3.9 Developing Algorithms
    • 3.10 Lists
    • 3.11 Binary Search
    • 3.12 Calling Procedures
    • 3.13 Developing Procedures
    • 3.14 Libraries
    • 3.15 Random Values
    • 3.16 Simulations
    • 3.17 Algorithmic Efficiency
    • 3.18 Undecidable Problems
  • Big Idea 4
    • 4.1 The Internet
    • 4.2 Fault Tolerant
    • 4.3 Parallel and Distributed Computing
  • Big Idea 5
    • 5.1 Beneficial and Harmful Effects
    • 5.2 Digital Divide
    • 5.3 Computing Bias
    • 5.4 Crowdsourcing
    • 5.5 Legal and Ethical Concerns
    • 5.6 Safe Computing
  • Code
    • Week 10
    • Week 11
    • Week 12
    • Week 13
    • Week 14
    • Week 15
    • Week 16
    • Week 17
    • Week 18
    • Week 19
    • Week 20
    • Week 21
    • Week 22
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  • Enduring Understanding
  • Learning Objective
  • Essential Knowledge

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  1. Big Idea 3

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.

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