Intermediate Topic 30 of 51 Theory & Discrete Math
Decidability
Whether an algorithm can always answer a yes/no question.
How it works
A problem is decidable if some TM always halts with the correct yes/no answer; recognizable if it halts on yes-instances. Most formal languages are undecidable by counting arguments.
Where it is used
Knowing what software can verify.
Common pitfall
Recognizable does not mean decidable.
Where it fits in the course
Decidability is topic 30 of 51 in Theory & Discrete Math, rated Intermediate. It follows Church-Turing Thesis. The next topic is Halting Problem.
Practice and explore
- Open the interactive lesson, with a mini quiz.
- Take the Theory & Discrete Math quiz.
How to study this topic
- Read the explanation above and restate the definition in your own words.
- Open the interactive lesson and answer its mini quiz.
- Read the common pitfall, then write a short example that avoids it.
- Check your understanding in the Theory & Discrete Math quiz, and revisit the topic if you miss a question.
Frequently asked questions
What is Decidability?
Whether an algorithm can always answer a yes/no question. It belongs to Theory & Discrete Math and is an intermediate-level topic.
Where do people use Decidability?
Knowing what software can verify.
What is the most common mistake with Decidability?
Recognizable does not mean decidable.
What should I learn before this topic?
Start with Church-Turing Thesis, the topic just before it in Theory & Discrete Math.
How can I practice it?
Answer the mini quiz in the interactive lesson, then take the Theory & Discrete Math quiz.
Is Decidability hard to learn?
It is an Intermediate topic. Be comfortable with the Beginner topics in this area first, then read the common pitfall carefully, since it is where most mistakes happen.
How long does it take to learn Decidability?
Most learners can read the explanation and finish the interactive lesson in under an hour. Fluency comes from applying the idea, so plan a few short practice sessions with the quiz.
Which topics are related to Decidability?
Church-Turing Thesis, Halting Problem, Turing Machines are closely connected. The full list is in the related topics section of this page.
What should I study after Decidability?
Continue with Halting Problem, the next topic in Theory & Discrete Math.
Related topics
- Church-Turing Thesis (Theory & Discrete Math)
- Halting Problem (Theory & Discrete Math)
- Turing Machines (Theory & Discrete Math)
- Reductions (Theory & Discrete Math)