What Language Does This Specific Grammar Produce?

[mathmari]

Hey!

Let G=(N,T,S,P) be a grammar with the non-terminal symbols N={S,E,T,Z,Q,C,D}, the terminal symbols T={0,1} and the production rules

P={ S  ->  E | Z | Q, 
    E  ->  1E | 0T | ε, 
    T  ->  1T | 0E, 
    Z  ->  1Z | 0E | ε, 
    Q  ->  CD, 
    C  ->  0C | 0, 
    D  ->  1D | 1}

How could we determine the language L(G) that the grammar produces? From the above rules we get for example the words [m]11010111010[/m], [m]11000110110[/m], [m]0000001111111[/m].

Is the language maybe $L(G)=\{w\in \{0,1\}^\star \mid \# 0 < \# 1\}$ ? (Wondering)

 

[Future Bruno]

The language $L(G)$ produced by the grammar G is the set of all strings in $\{0,1\}^*$ (the Kleene star closure of 0 and 1) that can be generated by the grammar. To determine this language, we can use a process known as "derivation". This involves starting with the start symbol S and replacing it with a right-hand side of one of its production rules. We then repeat this process for each of the symbols that we have generated until we get only terminal symbols. The strings that can be generated by this process will be the language $L(G)$.