Consider the language L = {a'bck | i + j,j # k, i + k}; it is not a context- freelanguage. Show that it nevertheless satisfies the conditions of the context-free pumpinglemma, that i s, show that there exists an m so that for all strings w in L of lengthat least m, we can write w = uvxyz with |vxy| < m, vy| > 1, such that Vi > 0 :uv'xy'z € L.

Pumping lemma for CFL is used to prove the language is not cfl using some valid string s. Never use…

Answered: Consider the language L = {a'b'c* | i #…

Computer Networking: A Top-Down Approach (7th Edition)

7th Edition

ISBN:9780133594140

Author:James Kurose, Keith Ross

Publisher:James Kurose, Keith Ross

Chapter1: Computer Networks And The Internet

Section: Chapter Questions

Problem R1RQ: What is the difference between a host and an end system? List several different types of end...

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Let A be the language of binary strings of even length that are also palindromes. That is, A is a language over the alphabet S={0,1} and win A if and only if the length of w is even and w is equal to the reverse of w. Use the pumping lemma for regular languages to prove that A is not regular.
For any string w 6=/ E, the principal suffix of w is the string resulting by removing the first symbol from w. We will denote this string by ps(w). For any language L, define ps(L) := {ps(w) : w ∈ L ∧ w 6=/ E}. Show that if L is regular, then ps(L) is regular. (The underlying alphabet is arbitrary.) Show by giving rules to transform a regex for L into a regex for ps(L).
Let ∑ = {a, b}. Given the language L = {b^n a^m: m,n≥0}, find the regular expression r such that L(r) = L.
on A language L is called slithy if it contains at least two strings and has the following property: For every two strings x, y in L such that |x|< lyl, the string obtained by taking the first letter of y and inserting it at the start of x is also in L. For example, if L contains aaa and baaba, then it must also contain the string baaa. Prove by contradiction that every slithy language contains two strings of the same length.
Question 1 Let LC * be a regular language over some alphabet Σ. The Kleene-closure L* of L is given by {V1V2 • Vn | n ≥ 0, V1, V2, . . . , Vn € L}. (a) Suppose DFA D = (Q, Σ, 8, qo, F) satisfies L(D) = L. Construct an NFA N = (Q', Σ, 8', %, F') such that L(N) = L*. L* (b) Prove by induction on n that each word v₁v2 Un with n ≥ 0, V₁, V2, ..., Un E L is accepted by the NFA N proposed in item (a). (c) Prove that each word accepted/recognized by the NFA N proposed in item (a) is a word of the language L*.
For any string w = w0w1w2 ...wn, the reverse of w, written wR, is the string in the reverse order, wnwn−1 ...w1w0. For any language L ⊆ Σ∗, we can define its reverse as LR = {wR | w ∈ L}. Show that if L is regular, then so is LR.
Let L be the language L={aPb9cds | pq and q#r} over the alphabet Σ={a,b,c,d). Prove that L is not regular using the pumping lemma. Note: Follow the mathematical formalism given in the textbook. Explain your steps.
on A language L is called slithy if it contains at least two strings and has the following property: For every two strings x, y in L such that |x|< lyl, the string obtained by taking the first letter of y and inserting it at the start of x is also in L. For example, if L contains aaa and baaba, then it must also contain the string baaa. Prove by contradiction that every slithy language contains two strings of the same length.
Let L be the language L={aPb9cds | pq and q#r} over the alphabet Σ={a,b,c,d). Prove that L is not regular using the pumping lemma. Note: Follow the mathematical formalism given in the textbook. Explain your steps.

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