TOC Grammer

Question

S-> aSb

What will the above grammar generates?Is it empty set?

Comments

Yes it will generate nothing, so an empty set.

Answer 1

"the language of G, denoted as L(G), is defined as all those sentences that can be derived in a finite number of steps from the start symbol S."

Starting with S, applying the production rule once to S gives aSb. Applying the rule twice gives aaSbb.

By applying the rule any finite number still gives non terminal symbol S. Since no sentences can be derived in a finite number of steps, the language is empty.