I am reading two books about the Turing Machine.
- "Computational Complexity" by Christos H. Papadimitriou.
- "Computational Complexity: A Modern Approach" by Sanjeev Arora and Boaz Barak.
However, the definitions in these books have a little differences and I do not figure out the relationship between the following concepts:
- A language is computable by a TM.
- A language can be decided by a TM.
What does the "language" exactly mean? A function or a set?
What is the relationship between them?
Is there a kind of containment relationship between them?