abstracttheoryregular-languagefsmpumping-lemma

How to read language definition syntax for regular/nonregular languages


I am trying to understand a simple concept about Language definition. Specifically when there are two strings in the language definition. such as:

    Language F = ww | w ∈ {0,1}*

Can someone help me understand the syntax? It makes sense to me when there is only one w, the set notation containing w also confuses me.
Looking it up online/in the book didn't answer this specific question concisely.


Solution

  • What this particular notation is telling you is that there is a language F of strings all the strings in F can be written in the form ww, where w is some string of binary digits. "ww" means that you take a string w and concatenate it with itself; so, if w=Patrick87, then ww=Patrick87Patrick87. Not all strings are of the form ww; for instance, consider "01". So, this definition tells us which strings are and which strings are not in F.