Parse Trees

Parse Trees

A parse tree is a tree structure that represents the syntactic structure of a string according to a given grammar. In computer science, parse trees are essential for understanding how context-free languages are generated and processed. A context-free grammar (CFG) defines the rules for generating strings in a language, and the parse tree visually represents these rules.

Understanding Parse Trees

A parse tree consists of nodes that represent grammar symbols. The root of the tree is the start symbol of the grammar. The internal nodes represent non-terminal symbols, and the leaf nodes represent terminal symbols (the actual symbols of the string).

Each internal node branches into child nodes according to the production rules of the grammar. The leaves of the tree form the string derived from the start symbol. The structure of the parse tree shows how the string can be derived step by step from the grammar.

Example of a Parse Tree

Consider the following context-free grammar:

S → AB
A → a
B → b

This grammar generates the string