language 𝐿 consisting of all strings

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Anu Bhardwaj · Accepted Answer

Regular Expression: L = b* ab* a + b* This expression defines a language (L) consisting of strings that can be formed in two ways: b followed by ab*a: * This means any number of "b"s followed by "ab" (where "a" and "b" can appear zero or more times) and then ending with an "a". Just b : * This includes strings with only zero or more "b"s. Non-deterministic Finite Automaton (NFA) Here's the NFA for the language L: States: q0: Start state q1: State reached after seeing any number of "b"s q2: Accepting state reached after seeing "ab*" followed by "a" Transitions: q0 -> q0 (on "b"): Allows any number of leading "b"s. q0 -> q1 (on "a"): Allows a single "a" at the beginning (becomes irrelevant later). q1 -> q1 (on "b"): Allows any number of "b"s in both options. q1 -> q2 (on "a"): If "b*" is seen, transition to q2 on seeing "a". q2 -> q2 (on any symbol): Once in q2, the automaton accepts any remaining symbols (including "b"). Start State: q0 Accepting States: q2 Regular Grammar Here's the regular grammar for the language L: Variables: S: Start symbol B: Represents zero or more "b"s (b*) A: Represents a single "a" Production Rules: S -> BAb | B (Vertical bar (|) denotes OR) B -> bB | ε (ε represents the empty string) This grammar reflects the two ways to form strings in L: S -> BAb: Matches the pattern "b ab a". S -> B: Matches the pattern "b*". Explanation: The B variable allows for any number of "b"s at the beginning. The Ab rule handles the "ab*a" part, where A represents the single ending "a". The empty string (ε) in the B production allows for strings with only "b"s. Both the NFA and the regular grammar capture the essence of the language L, allowing for strings with any number of leading "b"s followed by either "ab*a" or just more "b"s.

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Anu Bhardwaj

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