Language Generated by a Grammar

Given a grammar G with start symbol S , the language generated by G, denoted L(G) , is the set of derivable terminal strings w : L(G) = { w | S +⇒ w }

Two grammars that generate the same language are equivalent. a^*b^*(a | b)^* = (a | b)^*

The union of two languages is simply set union, i.e., L₁ ∪ L₂ = { l | l ∈ L₁ ∨ l ∈ L₂ }

The concatenation of two languages is: L₁L₂ = { l₁l₂ | l₁ ∈ L₁ ∧ l₂ ∈ L₂ }