Use the pumping lemma to show that the following languages are not regular.1. A₁ = {012 | n >= 0}2. A3 = {an | n >= 0}2^n(Here, a means a string of 2n a's.)

To show that the languages (A1={0n1n2n∣n≥0}) and (A3={a2n∣n≥0}) are not regular using the Pumping…

Answered: Use the pumping lemma to show that the…

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Use the Pumping Lemma to show the following language L is NOT regular. L= {w E (a, b, c}* ; where w has equal number of a's, b's, and c's}
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L1={u €E•[u ends with aa}. 12 = {u €E•[u ends and begins with different letters }. L3 = {u €I•|u contains abba). L4 = {u €E•[u is of the form anbamfor n,m> 0}. Given the above languages: (a) Use the set operators 'union' and 'complement' to describe L5 = L1 n L2. (b) Prove that L5 is regular.
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Theoretical computer science Hello i need help with this task, 2.Part: Let L1, L2 and L3 be the following languages above the alphabet Σ= {a,b}: L1 = {s1 • aa • s2 | s1, s2 ∈ Σ* }, L2 = {ambn | m, n ∈ IN and m < n}, L3 = {s ∈ Σ* | s does not contain the substring aa}. Subtask (a): Its given the following strings: u1 = ∈, u2 = ab, u3 = aab and u4 = bb. (i) For each of these character strings ui, give the suffix set assigned to itSL1 (ui) on.(ii) For each of these character strings ui, give the suffix set assigned to itSL2 (ui) on.(iii) For each of these character strings ui, give the suffix set assigned to itSL3 (ui) on. Subtask (b): Answer the following questions and give reasons for each of them detailed.(i) Which Nerode index does the language L1 have?(ii) Which Nerode index does the language L2 have?(iii) What is the Nerode index of language L3?
Computer Representation: Consider the bit string representation of sets A and B: (info in photo) Please help solve
Example 8: Show that the language L-{a' b"li>0} is not regular.
∑ = {C,A,G,T}, L = { w : w = CAjGnTmC, m = j + n }. For example, CAGTTC ∈ L; CTAGTC ∉ L because the symbols are not in the order specified by the characteristic function; CAGTT ∉ L because it does not end with C; and CAGGTTC ∉ L because the number of T's do not equal the number of A's plus the number of G's. Prove that L ∉ RLs using the RL pumping theorem.

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Use the pumping lemma to show that the following languages are not regular. 1. A₁ = {012 | n >= 0} 2. A3 = {an | n >= 0} 2^n (Here, a means a string of 2n a's.)