What are some examples of undecidable languages and how are they different from decidable languages?

Undecidable languages are languages for which there is no algorithm that can determine whether a given input string is in the language or not. Examples of undecidable languages include the Halting Problem and the Post Correspondence Problem.

Decidable languages, on the other hand, are languages for which there exists an algorithm that can determine whether a given input string is in the language or not. Examples of decidable languages include regular languages and context-free languages.

The key difference between undecidable and decidable languages is that decidable languages have algorithms that can always provide a definite answer, while undecidable languages do not have such algorithms.