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## Context-free grammars

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Context-free grammars represent language-generating rewriting systems. Each of their rewriting rules has a single symbol on its left-hand sides. By repeatedly applying these rules, these grammars generate sentences of their languages. This chapter gives a mathematical introduction into context-free grammars. First, Section 6.1 defines their basic versions. Then, Section 6.2 presents several mathematical methods that transform the basic versions so that the transformed versions are as powerful as the original versions but are much easier to handle in theory as well as in practice.

Chapter Contents:

• 6.1 Mathematical elements of context-free grammars
• 6.2 Canonical derivations and derivation trees
• 6.2.1 Leftmost derivations
• 6.2.2 Rightmost derivations
• 6.2.3 Derivation trees
• 6.2.4 Ambiguity
• 6.3 Useless symbols and their elimination
• 6.4 Erasing rules and their elimination
• 6.5 Single rules and their elimination
• 6.6 Chomsky normal form
• 6.7 Left recursion and its removal
• 6.7.1 Direct left recursion and its elimination
• 6.7.2 Left recursion and its elimination
• 6.7.3 Right recursion
• 6.8 Greibach normal form

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