# Language Decidability

What is the easiest and the most straightforward way to find whether a given language is decidable?

For example, how do we know if the following languages are decidable or not?

Binary representation of all prime numbers
{ empty string(eps) }

• If you can write a program that decides the language, then it's decidable. This captures your two examples. May 6 '18 at 22:03
• @YuvalFilmus How are they decidable? Can you explain plz? May 6 '18 at 22:55
• May 7 '18 at 11:05
• There isn't really an "easiest or most straightforward way". Any mathematical proof is a creative act: it's not a mechanized process where you can just apply some technique, turn the handle and a proof drops out. May 7 '18 at 12:12

A language $L$ is decidable if there is an algorithm that halts on every input, says Yes if the input belongs to $L$, and says No if the input doesn't belong to $L$.