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(2) The following questions are related to regular expression and regular language: (i) Let E= {a, b} and r,r2, r be regular expressions. Find all the regular ones from the following expressions: a, 1, a. p, a + b, r³, r* ·$, (($)) + rị + r2, ri + r2 + r1, r*), (r1, ra), {n + r2}, (n · r2) (ii) Let E= {a, b}. Given regular expressions r = a*b*, r' = ba(ab)* + ab*ba* and r" = (a + b)aa(a + b)*, find L(*), L(r'), and L(r"), the languages defined by r, r', r", respectively. (i) Let Σ= (α b (a) Given the language L = {b"a": m,n 2 0}, find the regular expression r such that L(r) = L. (b) Given the language L = {(ba)", a"™b", aa: m,n 2 0}, find the regular expression r such that L(r) = L. (c) Given the language L = {ba b"a, (ab)*, aa: n,m 2 0 and h 2 1}, find the regular expression r such that L(r) = L.

(2) The following questions are related to regular expression and regular language: (i) Let E= {a, b} and r,r2, r be regular expressions. Find all the regular ones from the following expressions: a, 1, a. p, a + b, r³, r* ·$, (($)) + rị + r2, ri + r2 + r1, r*), (r1, ra), {n + r2}, (n · r2) (ii) Let E= {a, b}. Given regular expressions r = a*b*, r' = ba(ab)* + ab*ba* and r" = (a + b)aa(a + b)*, find L(*), L(r'), and L(r"), the languages defined by r, r', r", respectively. (i) Let Σ= (α b (a) Given the language L = {b"a": m,n 2 0}, find the regular expression r such that L(r) = L. (b) Given the language L = {(ba)", a"™b", aa: m,n 2 0}, find the regular expression r such that L(r) = L. (c) Given the language L = {ba b"a, (ab)*, aa: n,m 2 0 and h 2 1}, find the regular expression r such that L(r) = L.

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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Transcription for Educational Website: --- **Educational Resource on Regular Expressions and Regular Languages** The following questions delve into the fundamentals of regular expressions and regular languages: 1. **Question Set (i):** - Consider \(\Sigma = \{a, b\}\) and let \(r_1, r_2, r\) be regular expressions. Identify all the regular expressions from the list below: - \(a\) - \(\lambda\) - \(\phi\) - \(a + b\) - \(r^3\) - \(r^* \cdot \phi\) - \((\phi) + r_1 + r_2\) - \(r_1 + r_2 + r_1\) - \(r^*\) - \((r_1, r_2)\) - \(\{r_1 + r_2\}\) - \((r_1 \cdot r_2)\) 2. **Question Set (ii):** - With \(\Sigma = \{a, b\}\), and given regular expressions: - \(r = a^*b^*\) - \(r' = ba(ab)^* + ab^*ba^*\) - \(r'' = (a + b)aa(a + b)^*\) - Determine the languages \(L(r)\), \(L(r')\), and \(L(r'')\), which are defined by the regular expressions \(r\), \(r'\), and \(r''\) respectively. 3. **Question Set (iii):** - Let \(\Sigma = \{a, b\}\). - (a) Given the language \(L = \{b^na^m: m, n \geq 0\}\), find the regular expression \(r\) that defines \(L(r) = L\). - (b) Given the language \(L = \{(ba)^ma^nb^n, aa: m, n \geq 0\}\), find the regular expression \(r\) such that \(L(r) = L\). - (c) Given the language \(L = \{ba^mb^na, \, (ab)^h, \, aa: \, n, \,
Transcribed Image Text:Transcription for Educational Website: --- **Educational Resource on Regular Expressions and Regular Languages** The following questions delve into the fundamentals of regular expressions and regular languages: 1. **Question Set (i):** - Consider \(\Sigma = \{a, b\}\) and let \(r_1, r_2, r\) be regular expressions. Identify all the regular expressions from the list below: - \(a\) - \(\lambda\) - \(\phi\) - \(a + b\) - \(r^3\) - \(r^* \cdot \phi\) - \((\phi) + r_1 + r_2\) - \(r_1 + r_2 + r_1\) - \(r^*\) - \((r_1, r_2)\) - \(\{r_1 + r_2\}\) - \((r_1 \cdot r_2)\) 2. **Question Set (ii):** - With \(\Sigma = \{a, b\}\), and given regular expressions: - \(r = a^*b^*\) - \(r' = ba(ab)^* + ab^*ba^*\) - \(r'' = (a + b)aa(a + b)^*\) - Determine the languages \(L(r)\), \(L(r')\), and \(L(r'')\), which are defined by the regular expressions \(r\), \(r'\), and \(r''\) respectively. 3. **Question Set (iii):** - Let \(\Sigma = \{a, b\}\). - (a) Given the language \(L = \{b^na^m: m, n \geq 0\}\), find the regular expression \(r\) that defines \(L(r) = L\). - (b) Given the language \(L = \{(ba)^ma^nb^n, aa: m, n \geq 0\}\), find the regular expression \(r\) such that \(L(r) = L\). - (c) Given the language \(L = \{ba^mb^na, \, (ab)^h, \, aa: \, n, \,
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