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2. Fix an alphabet Σ. For any string w with w|≥2, let skip(w) be the string obtained by removing the first two symbols of w. Define two operators on languages: 1(L) = {w € Σ*: skip (w) € L}, and f2(L) {skip(w) *: WEL a) Consider L' = L(bba*) over the alphabet Σ= {a, b}. Write a regular expression representing f₁(L'). Write another regular expression representing f₂(L'). b) Claim: for every regular language L the language f1(L) is regular. Clearly state whether the claim is TRUE or FALSE, and then prove your answer. c) Claim: for every regular language L the language f2(L) is regular. Clearly state whether the claim is TRUE or FALSE, and then prove your answer.

2. Fix an alphabet Σ. For any string w with w|≥2, let skip(w) be the string obtained by removing the first two symbols of w. Define two operators on languages: 1(L) = {w € Σ*: skip (w) € L}, and f2(L) {skip(w) *: WEL a) Consider L' = L(bba*) over the alphabet Σ= {a, b}. Write a regular expression representing f₁(L'). Write another regular expression representing f₂(L'). b) Claim: for every regular language L the language f1(L) is regular. Clearly state whether the claim is TRUE or FALSE, and then prove your answer. c) Claim: for every regular language L the language f2(L) is regular. Clearly state whether the claim is TRUE or FALSE, and then prove your answer.

Database System Concepts
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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2. Fix an alphabet Σ. For any string w with w|≥2, let skip(w) be the string obtained by removing the first two symbols of w. Define two operators on languages: 1(L) = {w € Σ*: skip (w) € L}, and f2(L) {skip(w) *: WEL a) Consider L' = L(bba*) over the alphabet Σ= {a, b}. Write a regular expression representing f₁(L'). Write another regular expression representing f₂(L'). b) Claim: for every regular language L the language f1(L) is regular. Clearly state whether the claim is TRUE or FALSE, and then prove your answer. c) Claim: for every regular language L the language f2(L) is regular. Clearly state whether the claim is TRUE or FALSE, and then prove your answer.
Transcribed Image Text:2. Fix an alphabet Σ. For any string w with w|≥2, let skip(w) be the string obtained by removing the first two symbols of w. Define two operators on languages: 1(L) = {w € Σ*: skip (w) € L}, and f2(L) {skip(w) *: WEL a) Consider L' = L(bba*) over the alphabet Σ= {a, b}. Write a regular expression representing f₁(L'). Write another regular expression representing f₂(L'). b) Claim: for every regular language L the language f1(L) is regular. Clearly state whether the claim is TRUE or FALSE, and then prove your answer. c) Claim: for every regular language L the language f2(L) is regular. Clearly state whether the claim is TRUE or FALSE, and then prove your answer.
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