4. Consider alphabet Σ = {0,1} and language Lo₁ = {we*: w=0"1" for some nonnegative n€Z}.Prove or disprove that for each language Lover Σ, if Ln Lo₁ = 0 and L is regular, then L is finite.

Detailed explanation: The statement is false. We can disprove it with a counterexample. Here's why:…

Answered: 4. Consider alphabet Σ = {0,1} 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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Similar questions

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.
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?
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.
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Consider alphabet Σ = {0,1}. Prove or disprove that for all languages L₁,L₂, L over Σ, if L₁ CL C L2 and L1,L2 are decidable, then L is decidable.
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Consider the language L = { |‡x such that ï ¤ L(M₁)~ L(M₂)}. Show that L is not decidable.
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*.

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4. Consider alphabet Σ = {0,1} and language Lo₁ = {we*: w=0"1" for some nonnegative n€Z}. Prove or disprove that for each language Lover Σ, if Ln Lo₁ = 0 and L is regular, then L is finite.