Production (computer science) | Wikipedia audio article
Channel: wikipedia tts
Date: 07/06/2019

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Production_(computer_science)


00:03:47 Grammar generation
00:08:04 See also



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SUMMARY
=======
A production or production rule in computer science is a rewrite rule specifying a symbol substitution that can be recursively performed to generate new symbol sequences.  A finite set of productions 
  
    
      
        P
      
    
    {\displaystyle P}
   is the main component in the specification of a formal grammar (specifically a generative grammar). The other components are a finite set 
  
    
      
        N
      
    
    {\displaystyle N}
   of nonterminal symbols, a finite set (known as an alphabet) 
  
    
      
        Σ
      
    
    {\displaystyle \Sigma }
   of terminal symbols that is disjoint from 
  
    
      
        N
      
    
    {\displaystyle N}
   and a distinguished symbol 
  
    
      
        S
        ∈
        N
      
    
    {\displaystyle S\in N}
   that is the start symbol.
In an unrestricted grammar, a production is of the form 
  
    
      
        u
        →
        v
      
    
    {\displaystyle u\to v}
   where 
  
    
      
        u
      
    
    {\displaystyle u}
   and 
  
    
      
        v
      
    
    {\displaystyle v}
   are arbitrary strings of terminals and nonterminals however 
  
    
      
        u
      
    
    {\displaystyle u}
   may not be the empty string. If 
  
    
      
        v
      
    
    {\displaystyle v}
   is the empty string, this is denoted by the symbol 
  
    
      
        ϵ
      
    
    {\displaystyle \epsilon }
  , or 
  
    
      
        λ
      
    
    {\displaystyle \lambda }
   (rather than leave the right-hand side blank). So productions are members of the cartesian product

  
    
      
        
          V
          
            ∗
          
        
        N
        
          V
          
            ∗
          
        
        ×
        
          V
          
            ∗
          
        
        =
        (
        
          V
          
            ∗
          
        
        ∖
        
          Σ
          
            ∗
          
        
        )
        ×
        
          V
          
            ∗
          
        
      
    
    {\displaystyle V^{*}NV^{*}\times V^{*}=(V^{*}\setminus \Sigma ^{*})\times V^{*}}
  ,where 
  
    
      
        V
        :=
        N
        ∪
        Σ
      
    
    {\displaystyle V:=N\cup \Sigma }
   is the vocabulary, 
  
    
      
        
          

          
          
            ∗
          
        
      
    
    {\displaystyle {}^{*}}
   is the Kleene star operator, 
  
    
      
        
          V
          
            ∗
          
        
        N
        
          V
          
            ∗
          
        
      
    
    {\displaystyle V^{*}NV^{*}}
   indicates concatenation, and 
  
    
      
        ∪
      
    
    {\displaystyle \cup }
   denotes set union. If we do not allow the start symbol to occur in 
  
    
      
        v
      
    
    {\displaystyle v}
   (the word on the right side), we have to replace 
  
    
      
        
          V
          
            ∗
          
        
      
    
    {\displaystyle V^{*}}
   by 
  
    
      
        (
        V
        ∖
        {
        S
        }
        
          )
          
            ∗
          
        
      
    
    {\displaystyle (V\setminus \{S\})^{*}}
   on the right side of the cartesian product symbol.The other types of formal grammar in the Chomsky hierarchy impose additional restrictions on what constitutes a production. Notably in a context-free grammar, the left-hand side of a production must be a single nonterminal symbol. So productions are of the form ...