Checking a grammar/langauge is regular or not ?

In this tutorial we will discuss how to decide whether a perticular grammar/langauge is regular or not.
So follow given steps:

  1. Every finite language is regular that means if there is a limit to the language then it is regular.
    For example the language, L = { a20b20} is regular langauge whereas,
    Langauge, L = { anbn| n > 0} is not regular.
  2. Second case is if there is an infinite languge then we will check whether its DFA can be created. If no then it will not be a regular language
    And also we must have a pattern in the language otherwise FA cannot be created.

    Example
    Suppose given language, L = {ab, abab, ababab, ....}
    As we can see that there is a pattern in the language that is (ab)n
    So we can create FA for it as follows

    Cleary it is NFA so we are good to say that the language given is a regular language.
  3. String length should be in arithmetic progression

Rest of things will get clear using examples in next pages