Final Answer:
The language L(G) generated by the context-free grammar (G) s not regular.
Step-by-step explanation:
To determine the language L(G) generated by the context-free grammar (G), we need to find the set of terminal strings that can be derived from the start symbol (S) using the production rules provided.
The grammar G=({S,A,B},{a,b},{S→A∣aB,A→b,B→Sa},S) consists of three non-terminals S, A, and B, with terminals a and b. Starting from the start symbol (S), the production rules allow for the generation of strings in the language. Specifically, S can derive either (A) or (aB), (A) can derive (b), and (B) can derive (Sa).
However, analyzing the production rules reveals that the grammar contains recursive productions that involve the non-terminal (S). This recursion results in strings of arbitrary length, making it impossible to create a deterministic finite automaton (DFA) to recognize L(G). Regular languages are recognized by DFAs, but the presence of recursion violates the key property required for a language to be regular.
Hence, based on the properties of regular languages and the structure of the grammar (G), it can be concluded that L(G) is not regular. The grammar's recursive nature leads to an infinite number of possible strings, which cannot be recognized by a finite-state automaton, establishing the non-regularity of L(G).