3. Are the following languages A and B over the alphabet = {a, b, c, d} regular or nonreg- ular? For a language that is regular, give a regular expression that defines it. • For a nonregular language, using the pumping lemma prove that it is not regular. (a) (b) A = {a³fk+2+1 |j≥ 1, k≥ 1, m > 1}U {b'cs+2+¹ \r>t≥ 1, s≥ 1}. B = {a³+³f²k+2m|j≥ 1, k ≥ 1, m≥ 1}U {br+3c³d²t-¹|r≥ 1, s ≥ 1, t ≥ 1} Hints: The languages A and B are each expressed as a union of two sets. If one (or both) of the sets is non-regular, this does not imply anything about the non-regularity of the union. When trying to show that a language C is non-regular, we have to apply the pumping lemma to the entire language C (and not to the components of the union). On the other hand, if trying to show that C is regular, you can give regular expressions for the two component sets and then apply "+".

3. Are the following languages A and B over the alphabet = {a, b, c, d} regular or nonreg- ular? For a language that is regular, give a regular expression that defines it. • For a nonregular language, using the pumping lemma prove that it is not regular. (a) (b) A = {a³fk+2+1 |j≥ 1, k≥ 1, m > 1}U {b'cs+2+¹ \r>t≥ 1, s≥ 1}. B = {a³+³f²k+2m|j≥ 1, k ≥ 1, m≥ 1}U {br+3c³d²t-¹|r≥ 1, s ≥ 1, t ≥ 1} Hints: The languages A and B are each expressed as a union of two sets. If one (or both) of the sets is non-regular, this does not imply anything about the non-regularity of the union. When trying to show that a language C is non-regular, we have to apply the pumping lemma to the entire language C (and not to the components of the union). On the other hand, if trying to show that C is regular, you can give regular expressions for the two component sets and then apply "+".

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

1. Given L₁ = {a, abc, ac} and L₂ = {ab, c ba} are the languages over Σ = {a,b,c}, determine L₁ L₂ Obtain the regular expressions for the set (b, b, b,..), using the appropriate Kleene's closure.
3. Consider the languages = { ba" a b" |n > 0} a.) Use the Pumping Lemma for Regular Languages to show L is not Regular b.) Use the Myhill-Nerode Theorem to show L is not Regular.
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