I'm just starting to get into the theory of computation, which studies what can be computed, how quickly, using how much memory and with which computational model.

I have a pretty basic question, but am really hoping some of you guys can help me understand the concept behind it:

Why is everything centered around the notion and definition of LANGUAGES (i.e. regular languages and context free languages)? And how do these relate and describe the complexity of an algorithm and the possible computational models for solving them?

I read these sort of related questions:

• http://cstheory.stackexchange.com/questions/14811/what-is-the-enlightenment-im-supposed-to-attain-after-studying-finite-automata
• http://cstheory.stackexchange.com/questions/8539/how-practical-is-automata-theory

but still don't have an answer to my doubts, since they provide a practical justification of why they are important (which I do understand) but don't help me understand why complexity theory is based upon them.

I'm just starting to get into the theory of computation, which studies what can be computed, how quickly, using how much memory and with which computational model.

I have a pretty basic question, but am really hoping some of you guys can help me understand the concept behind it:

Why is everything centered around the notion and definition of LANGUAGES (i.e. regular languages and context free languages)? And how do these relate and describe the complexity of an algorithm and the possible computational models for solving them?

I read these sort of related questions:

• https://cstheory.stackexchange.com/questions/14811/what-is-the-enlightenment-im-supposed-to-attain-after-studying-finite-automata
• https://cstheory.stackexchange.com/questions/8539/how-practical-is-automata-theory

but still don't have an answer to my doubts, since they provide a practical justification of why they are important (which I do understand) but don't help me understand why complexity theory is based upon them.