In the Theory of automata, languages can be defined with different techniques. Some of these are mentioned below;
- Language definition by using the Descriptive definition
- Language definition by using the Recursive definition
- Language definition by using the Regular Expressions (RE)
- Language definition by using the Finite Automaton(FA)
What is Recursive definition of languages?
Three steps are required in recursive definition of a language.
Step 1: Need to define some basic words in the language.
Step 2: Need to define rules for constructing more words in the language.
Step 3: The strings constructed in step 1 and step 2 are valid strings, all other string are invalid and not to be a part of language.
Example of Recursive definition of languages
Recursive definition of EVEN length strings
Step 1: 2 is in EVEN.
Step 2: If x is in EVEN then x+2 and x-2 are EVEN. For example, if 2 is even then, 4 is also even number.
Step 3:
The strings constructed in step 1 and step 2 are valid strings (for example 2, 4, 6, 8,….)
All other string are invalid and not to be a part of language. (for example 1, 3, 5, 7, 9,….)