Consider alphabet Σ = {0,1,2,3} and language L = {w€Σ* : w = 0"1" 2" 3" for some positive m‚n €or disprove that L is context-free.Z}. Prove

Claim: The language L = {w ∈ Σ* : w = 0^m 1^n 2^m 3^n for some positive m, n ∈ Z} is not…

Answered: Consider alphabet Σ = {0,1,2,3} and…

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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Consider the language L = {a'bck | i + j,j # k, i + k}; it is not a context- free language. Show that it nevertheless satisfies the conditions of the context-free pumping lemma, that i s, show that there exists an m so that for all strings w in L of length at least m, we can write w = uvxyz with |vxy| 1, such that Vi > 0 : uv'xy'z € L.
Consider the language L = {a i b j c k | i 6= j, j 6= k, i 6= k}; it is not a context- free language. Show that it nevertheless satisfies the conditions of the context-free pumping lemma, that i s, show that there exists an m so that for all strings w in L of length at least m, we can write w = uvxyz with |vxy| ≤ m, |vy| ≥ 1, such that ∀i ≥ 0 : uvixyi z ∈ L.
Consider alphabet Σ = {0,1} and language Lo₁ = {weΣ* : w=0"1" for some nonnegative n€ Z}. Prove or disprove that for each language L over Σ, if L n Lo₁ = 0 and L is regular, then L is finite.
Suppose that relations R and S have n tuples and m tuples respectively. What is the minimum number of tuples that the results of the following expression can have? oc(R) × S, for some condition C. A. n*m B. min{n,m} С.n D. 0 E. m F. n-m G. n+m H. max{n,m}
Let Σ={a, b}. Let L be the language of all strings that contain two b's in their middle third. In other words, L= {xyz |x, z ∈ Σ* and y∈ Σ*bΣ*bΣ*, where |x|=|z|>=|y| }. Show that L is not a CFL
Suppose L is a language over {a,b}, and there is a fixed integer k such that for every x ∈ Σ*, xz ∈ L for some string z with |z| ≤ k. Does it follow that there is an FA accepting L? Why or why not?
w W 2. Consider alphabet Σ = regular. {0,1} and language L = {wer : [w; # Σ Σ (1 - w;)). Prove or disprove that L is i=1 i=1
Construct a graphical representation of DFA that accepts L={w∈(a+b)*: na(w) is even, nb(w)>1}no need to include explanations, just the graphical DFA.Please note that “a”s don't need to be consecutive.
Suppose L is a non empty regular language, over Σ, such that every w E L satisfies |w] =k, for some ke N. Show that there cannot exist a DFA M = (E, Q, 8, q0, F), where |Q| = k.
Let E = {a, b, #} and L = {w |w can be written as t#s#t with s, t e {a, b}*}. Show that L is not regular. Show that L is context-free.
Use the pumping lemma to prove that the following language is not context-free. Show all cases on Canvas L={a"b/ck | k =j*n}
Please explain your answer for both questions. For the first part n is greater than or equal to zero

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Consider alphabet Σ = {0,1,2,3} and language L = {w€Σ* : w = 0"1" 2" 3" for some positive m‚n € or disprove that L is context-free. Z}. Prove