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| 1.V is a finite set called the variables, 2. is a finite set, disjoint from V, called the terminals, 3.R is a finite set of rules, with each rule being a variable and a string of variables and terminals, and 4.S∈V is the start variable |
1. Element $$V$$$ is a finite set called the variables, 1. Element $$\Sigma$$ is a finite set, disjoint from [[latex2($V$)]], called the terminals, 1. Element $$R$$ is a finite set of rules, with each rule being a variable and a string of variables and terminals, and 1. Element $$S \in V$$ is the start variable An example of a rule is $$A \rightarrow aBa$$ $$B \rightarrow \epsilon$$ |
Context Free Grammar
Def: For every ContextFreeLanguage there is a ContextFreeGrammar that generates it and a PushDownAutomata that recognizes it.
A context-free grammar is a 4-tuple latex2($(V,\Sigma,R,S)$), where
- Element
$ is a finite set called the variables, Element
is a finite set, disjoint from latex2($V$), called the terminals, - Element
is a finite set of rules, with each rule being a variable and a string of variables and terminals, and - Element
is the start variable
An example of a rule is