Simplification of a Context-Free Grammar (CFG) typically involves several steps to reduce its complexity while preserving its language:

1. Removing Useless Symbols:
Non-generating Symbols: Symbols that cannot derive any string in the language of the grammar.
Non-reachable Symbols: Symbols that cannot be reached from the start symbol.

2. Unit Production Removal:
Unit productions are rules of the form \( A \rightarrow B \), where \( A \) and \( B \) are non-terminal symbols. These can be replaced with the productions of \( B \), effectively eliminating the unit productions.

3. Chaining of Productions:
Sometimes, non-terminal symbols can appear in chains of unit productions (e.g., \( A \rightarrow B \rightarrow C \)). These can be replaced by direct productions from \( A \) to \( C \), avoiding intermediary steps.

4. Simplifying Right-Hand Sides:
Ensuring that right-hand sides of productions are as simple as possible, often by eliminating unnecessary non-terminal symbols or grouping similar rules together.

5. Epsilon (ε)-Productions Handling:
Removing or handling productions that derive the empty string (\( \epsilon \)) appropriately, without affecting the language generated by the grammar.

6. Factoring Productions:
Grouping common prefixes or suffixes in productions to reduce redundancy and simplify the grammar.

7. Removing Useless Productions:
Productions that do not contribute to generating any terminal string (especially when combined with steps 1 and 2).

Each of these steps aims to streamline the CFG without changing the language it generates. The goal is to make the grammar easier to analyze, understand, and work with while maintaining its essential properties.