Question

A context-free grammar G=(V,T,S,P) is said to be a simple grammar or s-grammar if all its productions are of the form A→ax, where A∈V,a∈T,x∈V∗, and any pair (A,a) occurs at most once in P. Find a s-grammar for the following language. L={anbn+1∣n≥1}.

Answer 1

To create a simple grammar for the language L = anbn+1 , we need to define a set of productions that generate strings in the form anbn+1. The grammar G=(V,T,S,P) can be defined as S → aSb and S → ab.

Step-by-step explanation:

To create a simple grammar for the language L = anbn+1 , we need to define a set of productions that generate strings in the form anbn+1. Let's start with the start symbol S and create the following productions:

1. S → aSb
2. S → ab

It is possible to create strings with a 'a' and any number of 'b's' after it using the first production, while the second production only creates the string 'ab'. Since these productions are of the form A → ax, where x is a sequence of zero or more non-terminal symbols, and A is a non-terminal symbol, they meet the requirements for an s-grammar.