I am taking an Automata class, and I learnt that languages can be defined either recursively or by using regular expressions. I was introduced to both methods, and I learnt that Regex method is better and recursive method is outdated. I practiced some problems for recursive language definition (like defining Arithmetic Expressions and Polynomials recursively). However, I could not find more on this topic. I have searched many Automata books on internet, and almost all of them ignore this topic and focus on Regex method for describing languages. Is there any material with good information on the recursive method and practice problems for defining languages recursively?
What I mean by recursive methods is the three step method of the form
- a is in language L
- If x is a word in L, then so is xa
- Only those words defined by above rules are in L
The above method defines language L = {a aa aaa aaaa aaaaa......}