Question 2 1. Let L by a language over E. For each of the following statements about L, determine whether or not the statement is stronger, weaker or equivalent to L being regular i.e. does the state- ment (i) imply that L is regular, (ii) follow from L being regular, or (iii) both? You should justify your answer. (a) Lis finite. (b) E*\L is regular. (c) L* is regular. (d) L contains a regular language i.e. there exists a regular language Li C E* such that L C L. (e) Lis contained in a regular language i.e. there exists a regular language L2 C E* such that L C L2.
Question 2 1. Let L by a language over E. For each of the following statements about L, determine whether or not the statement is stronger, weaker or equivalent to L being regular i.e. does the state- ment (i) imply that L is regular, (ii) follow from L being regular, or (iii) both? You should justify your answer. (a) Lis finite. (b) E*\L is regular. (c) L* is regular. (d) L contains a regular language i.e. there exists a regular language Li C E* such that L C L. (e) Lis contained in a regular language i.e. there exists a regular language L2 C E* such that L C L2.
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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![Question 2
1. Let L by a language over E. For each of the following statements about L, determine whether
or not the statement is stronger, weaker or equivalent to L being regular i.e. does the state-
ment (i) imply that L is regular, (ii) follow from L being regular, or (iii) both? You should
justify your answer.
(a) Lis finite.
(b) E*\L is regular.
(c) L* is regular.
(d) L contains a regular language i.e. there exists a regular language Li C E* such that
L C L.
(e) Lis contained in a regular language i.e. there exists a regular language L2 C £* such
that L C L2.
2. Suppose that Land M are two languages over the same alphabet E. Show that the following
statements hold:
(a) LC L*
(b) If LC M* then L* C M*
(c) (L*)* = L*
(d) If L CM then L* C M*](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4dd952c9-a85e-47f8-a17e-0bac8b8d5ca3%2Fa3612f7d-dfcc-4064-8d8b-e72a9c866f0c%2Fsd8l5n_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Question 2
1. Let L by a language over E. For each of the following statements about L, determine whether
or not the statement is stronger, weaker or equivalent to L being regular i.e. does the state-
ment (i) imply that L is regular, (ii) follow from L being regular, or (iii) both? You should
justify your answer.
(a) Lis finite.
(b) E*\L is regular.
(c) L* is regular.
(d) L contains a regular language i.e. there exists a regular language Li C E* such that
L C L.
(e) Lis contained in a regular language i.e. there exists a regular language L2 C £* such
that L C L2.
2. Suppose that Land M are two languages over the same alphabet E. Show that the following
statements hold:
(a) LC L*
(b) If LC M* then L* C M*
(c) (L*)* = L*
(d) If L CM then L* C M*
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