<Li> No other languages over Σ are regular . </Li> <P> See regular expression for its syntax and semantics . Note that the above cases are in effect the defining rules of regular expression . </P> <P> All finite languages are regular; in particular the empty string language (ε) = Ø * is regular . Other typical examples include the language consisting of all strings over the alphabet (a, b) which contain an even number of as, or the language consisting of all strings of the form: several as followed by several bs . </P> <P> A simple example of a language that is not regular is the set of strings (a b n ≥ 0). Intuitively, it cannot be recognized with a finite automaton, since a finite automaton has finite memory and it cannot remember the exact number of a's . Techniques to prove this fact rigorously are given below . </P>

Closure properties of regular languages in theory of computation