Lecture 3 - Context-Free Grammar CFG

A context-free grammar (CFG) is a set of recursive rules used to generate patterns of strings. A CFG \(G = (V, \Sigma, R, S)\) consists of:

• A finite set of variables (non-terminal symbols) \(V\).
• A finite set of terminal symbols \(\Sigma\).
• S \(\in\) \(V-\Sigma\) is the start symbol.

• R \(\in\) \((V-\Sigma) \times (U)^*\) is a finite set of rules.

• Define in one step:

• derivation
• G generates \(w\in \Sigma^*\) if \(S \Rightarrow^* w\).
• L(G) = {w \(\in \Sigma ^*\)| G generates w} is a context-free language.

Example:

• \(\{a^nb^n|n\geq 0\}\) is a context-free language.
• Rule: \(S \rightarrow aSb | e\).
• \(\{w\in {a,b}^*|w = w^R\}\) is a context-free language.
• Rule: \(S \rightarrow aSa | bSb | e | a | b\).

---

最后更新: 2024年9月30日 11:27:07
创建日期: 2024年9月30日 11:27:07