4) Consider the language L = L₁ L2, where L₁ = {ww: w = {a, b}* and L2 = {a”b*a": n≥ 0}. a) List the first four strings in the lexicographic enumeration of L? b) Write a context-free grammar to generate L. c) Show a natural PDA for L. (In other words, don't just build it from the grammar using one of the two-state constructions presented in this chapter.) d) Prove that L is not regular. 1) Build a PDA to accept each of the following languages L: a) BalDelim = {w where w is a string of delimiters: (, ), [, ], {, }, that are properly balanced}. b) {ab2i3j + 1}. c) {w = {a, b}* : #a(w) = 2•#b(w)}. d) {a"b" m≤n≤2m}. e) {w = {a, b}* w = w²}. f) {abci,j, k ≥ 0 and (i #j orj #k)}. g) {we {a, b}* : every prefix of w has at least as many a's as b's}. h) {aba" n, m ≥ 0 and m is even}.
4) Consider the language L = L₁ L2, where L₁ = {ww: w = {a, b}* and L2 = {a”b*a": n≥ 0}. a) List the first four strings in the lexicographic enumeration of L? b) Write a context-free grammar to generate L. c) Show a natural PDA for L. (In other words, don't just build it from the grammar using one of the two-state constructions presented in this chapter.) d) Prove that L is not regular. 1) Build a PDA to accept each of the following languages L: a) BalDelim = {w where w is a string of delimiters: (, ), [, ], {, }, that are properly balanced}. b) {ab2i3j + 1}. c) {w = {a, b}* : #a(w) = 2•#b(w)}. d) {a"b" m≤n≤2m}. e) {w = {a, b}* w = w²}. f) {abci,j, k ≥ 0 and (i #j orj #k)}. g) {we {a, b}* : every prefix of w has at least as many a's as b's}. h) {aba" n, m ≥ 0 and m is even}.
C++ Programming: From Problem Analysis to Program Design
8th Edition
ISBN:9781337102087
Author:D. S. Malik
Publisher:D. S. Malik
Chapter18: Stacks And Queues
Section: Chapter Questions
Problem 3PE
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Transcribed Image Text:4) Consider the language L = L₁ L2, where L₁ = {ww: w = {a, b}* and L2 = {a”b*a": n≥ 0}.
a)
List the first four strings in the lexicographic enumeration of L?
b) Write a context-free grammar to generate L.
c) Show a natural PDA for L. (In other words, don't just build it from the grammar using one of the two-state
constructions presented in this chapter.)
d) Prove that L is not regular.
![1) Build a PDA to accept each of the following languages L:
a)
BalDelim = {w where w is a string of delimiters: (, ), [, ], {, }, that are properly balanced}.
b) {ab2i3j + 1}.
c) {w = {a, b}* : #a(w) = 2•#b(w)}.
d) {a"b" m≤n≤2m}.
e)
{w = {a, b}* w = w²}.
f) {abci,j, k ≥ 0 and (i #j orj #k)}.
g) {we {a, b}* : every prefix of w has at least as many a's as b's}.
h) {aba" n, m ≥ 0 and m is even}.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F36fd9238-414f-4e5e-b00a-4398e187562f%2F55d25734-3d6f-413e-97a3-d98dcfd5d151%2F8emikfs_processed.png&w=3840&q=75)
Transcribed Image Text:1) Build a PDA to accept each of the following languages L:
a)
BalDelim = {w where w is a string of delimiters: (, ), [, ], {, }, that are properly balanced}.
b) {ab2i3j + 1}.
c) {w = {a, b}* : #a(w) = 2•#b(w)}.
d) {a"b" m≤n≤2m}.
e)
{w = {a, b}* w = w²}.
f) {abci,j, k ≥ 0 and (i #j orj #k)}.
g) {we {a, b}* : every prefix of w has at least as many a's as b's}.
h) {aba" n, m ≥ 0 and m is even}.
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