Properly Nested Parentheses and Curly Braces: Recursive Definition

What is a recursive definition for strings of properly nested parentheses and curly braces?

Give a recursive definition for strings of properly nested parentheses and curly braces.

Answer:

A recursive definition for strings of properly nested parentheses and curly braces is when a string is either empty or starts with an opening parenthesis/curly brace followed by a properly nested string followed by the corresponding closing parenthesis/curly brace.

To provide a recursive definition for strings of properly nested parentheses and curly braces, we can define the base case and the recursive step. The base case is that an empty string is considered to be properly nested. The recursive step is that if a string starts with an opening parenthesis "(" followed by a properly nested string, followed by a closing parenthesis ")", it is considered to be properly nested. Similarly, if a string starts with an opening curly brace "{" followed by a properly nested string, followed by a closing curly brace "}", it is considered to be properly nested.

Therefore, a recursive definition for strings of properly nested parentheses and curly braces is characterized by the pattern where a string starts with an opening parenthesis or curly brace, followed by a properly nested string, and ending with the corresponding closing parenthesis or curly brace.