Recursive definition of Palindromes

Language of Palindromes Over {a, b}

  • Base Case: The empty string ε, a, and b are in the language LLL.
  • Recursive Step:
    • If xxx is in LLL, then a⋅x⋅aa \cdot x \cdot aa⋅x⋅a and b⋅x⋅bb \cdot x \cdot bb⋅x⋅b are in LLL.
  • Closure: A string is in LLL if and only if it can be derived from the base case using a finite number of applications of the recursive step.