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Let the following languages Li be given over the alphabet 2= {0, I, 2}. %3D . Li - u.2 |υε Σ' %3D . L(1l . υ | υ ε Σ! • L3 = {2"10" | n e N} %3D • L4 = {0"12n+m | n, m E N} %3D

Let the following languages Li be given over the alphabet 2= {0, I, 2}. %3D . Li - u.2 |υε Σ' %3D . L(1l . υ | υ ε Σ! • L3 = {2"10" | n e N} %3D • L4 = {0"12n+m | n, m E N} %3D

Computer Networking: A Top-Down Approach (7th Edition)
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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Let the following languages Li be given over the alphabet E = {O, I, 2}. . L1-u-2 | υε Σ') . L- 11 . υ | υ ε Σ} V • L3 = {2"10" | n € N} • L4 = {0"12"+m | n, m E N} Subtask (a) Answer the following question and give a reason for your answer. Which of these languages Li has a Nerode index greater than or equal to three? Subtask (b) Reason that the two languages LI and L2 have a finite Nerode index. Subtask (c) In order to justify that the language L3 has an infinite Nerode index, one must specify an infinite number of character strings uj from E* to which different sets of suffixes SL3 (uj) are assigned in pairs. For this purpose it is advisable to choose the character string uj = 2-1 for each je IN. Answer the following questions. (i) State how many and which character strings from E*the one String contains the suffix set ŞL3 (uj) assigned to uj. Kii) Explain why it follows from j1 #ja that the suffix sets assigned to the two strings ujl and uj2 are different, ie. H. that SL3 ujil ESL3 (uja) holds Subtask (d) Explain why the language L4 has an infinite Nerode index. Hint: Select - in analogy to subtask (c) - an infinite number of strings uj and explain why the strings you have selected are assigned different sets of suffixes SL4 (uj) in pairs
Transcribed Image Text:Let the following languages Li be given over the alphabet E = {O, I, 2}. . L1-u-2 | υε Σ') . L- 11 . υ | υ ε Σ} V • L3 = {2"10" | n € N} • L4 = {0"12"+m | n, m E N} Subtask (a) Answer the following question and give a reason for your answer. Which of these languages Li has a Nerode index greater than or equal to three? Subtask (b) Reason that the two languages LI and L2 have a finite Nerode index. Subtask (c) In order to justify that the language L3 has an infinite Nerode index, one must specify an infinite number of character strings uj from E* to which different sets of suffixes SL3 (uj) are assigned in pairs. For this purpose it is advisable to choose the character string uj = 2-1 for each je IN. Answer the following questions. (i) State how many and which character strings from E*the one String contains the suffix set ŞL3 (uj) assigned to uj. Kii) Explain why it follows from j1 #ja that the suffix sets assigned to the two strings ujl and uj2 are different, ie. H. that SL3 ujil ESL3 (uja) holds Subtask (d) Explain why the language L4 has an infinite Nerode index. Hint: Select - in analogy to subtask (c) - an infinite number of strings uj and explain why the strings you have selected are assigned different sets of suffixes SL4 (uj) in pairs
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