Language

a language $A$ over an Alphabet $\Sigma$ is a set of strings over $\Sigma$. $A$ is a subset of ${\Sigma }^{\ast }$.

problem encoding

any problem can be encoded as a language, that is, represented as a set of strings belonging to $A$. these strings are considered accepted.

regular language

if the set of strings that an Automata $M$ accepts is equal to a language $A$, then $A$ is said to be regular. A language can also be not regular, meaning a DFA cannot be constructed for it.

See Regular languages.

set construction

when constructing a set, we can define arbitrary functions that help us simplify stuff. for example, we can say that $count(w,\sigma )$ tells us how many times $\sigma$ occurs in string $w$.