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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 [[latex2($V$)]] is a finite set called the variables, 1. Element [[latex2($\Sigma$)]] is a finite set, disjoint from [[latex2($V$)]], called the terminals, 1. Element [[latex2($R$)]] is a finite set of rules, with each rule being a variable and a string of variables and terminals, and 1. Element [[latex2($S \in V$)]] is the start variable An example of a rule is {{latex2($A \rarrow aBa$) latex2($B \rarrow \epsilon$) }} |
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 latex2($V$) is a finite set called the variables,
Element latex2($\Sigma$) is a finite set, disjoint from latex2($V$), called the terminals,
Element latex2($R$) is a finite set of rules, with each rule being a variable and a string of variables and terminals, and
Element latex2($S \in V$) is the start variable
An example of a rule is
{{latex2($A \rarrow aBa$) latex2($B \rarrow \epsilon$) }}