Successfully reported this slideshow.
We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime.

Introduction to Computer theory (Automata Theory) 2nd Edition By Denial I.A. COHEN. Chapter 2 Problems

24,790 views

Published on

solution to some problems of Automata

Published in: Data & Analytics
  • I’ve personally never heard of companies who can produce a paper for you until word got around among my college groupmates. My professor asked me to write a research paper based on a field I have no idea about. My research skills are also very poor. So, I thought I’d give it a try. I chose a writer who matched my writing style and fulfilled every requirement I proposed. I turned my paper in and I actually got a good grade. I highly recommend ⇒ www.HelpWriting.net ⇐
       Reply 
    Are you sure you want to  Yes  No
    Your message goes here
  • Did you try ⇒ www.HelpWriting.net ⇐?. They know how to do an amazing essay, research papers or dissertations.
       Reply 
    Are you sure you want to  Yes  No
    Your message goes here
  • Writing a good research paper isn't easy and it's the fruit of hard work. You can get help from writing. Check out, please HelpWriting.net
       Reply 
    Are you sure you want to  Yes  No
    Your message goes here
  • What if you had a printing press that could spit out hundred dollar bills on demand? Do you think that would change your life? ●●● http://t.cn/AisJWYf4
       Reply 
    Are you sure you want to  Yes  No
    Your message goes here
  • Making a living taking surveys at home! I have been a stay at home mom for almost 5 years and I am so excited to be able to still stay home, take care of my children and make a living taking surveys on my own computer! It's so easy to get started and I plan to make enough money each week so that my husband can actuallly quit his second job!!! Thank you so much! ●●● https://bit.ly/2Ruzr8s
       Reply 
    Are you sure you want to  Yes  No
    Your message goes here

Introduction to Computer theory (Automata Theory) 2nd Edition By Denial I.A. COHEN. Chapter 2 Problems

  1. 1. By: F.A 4/1/2014 AUTOMATA CHAPTER 2: LANGUAGES (PROBLEMS)
  2. 2. Chapter 2: LANGUAGES Problems: 1. Consider the language S*, where S = {a, b}. How many words does this language have of length 2? Of length 3? Of length n? Solution: S = {a, b} S* = {, a, b, aa, ab, bb, ba, aaa, aab, aba, abb, bbb, bba, bab, baa,…. }  So this language have words of length 2 = 4 Of length 3 = 8 Of length n = 2n  We can solve this question in the following way too Let number of words = nm Then words of length 2 = 22 = 4 Of length 3 = 23 = 8 Of length n = 2n 2. Consider the language S*, where S = {aa, b}. how many words does this language have of length 4? Of length 5? Of length 6? What can be said in general? Solution: S = {aa, b} S* = {, aa, b, aaaa, aab, bb, baa, aaaaaa, aaaab, aabb, aabaa, baaaa, baab, bbb, bbaa, aaaaaaaa, aaaaaab, aaaabb, aaaabaa, aabaaaa, aabaab, aabbb, aabbaa,
  3. 3. bbbb, bbbaa, bbaaaa, bbaab, baabb, baabaa, baaaaaa, baaaab, aaaaaaaaaa, …….}  So words of length 4 = 24 = 16 Of length 5 = 25 = 32 Of length 5 = 26 = 64 In general: In general we can say that 3. Consider the language S*, where S = {ab, ba}. Write out all the words in S* that have seven or fewer letters. Can any word in this language contain the substrings aaa or bbb? What is the smallest word that is not in this language? Solution: S = {ab, ba} S* = {, ab, ba, abab, abba, baba, baab, ababab, ababba, abbaba, abbaab, baabab, baabba, bababa, babaab, abababab, abababba, ababbaba, ababbaab, abbaabab, abbaabba, abbababa, abbabaab, baababab, baababba, baabbaba, baabbaab, babaabab, babaabba, babababa, bababaab, ababababab, ababababba, abababbaba, abababbaab, ababbaabab, ababbaabba, ababbababa, ababbabaab, abbaababab, abbaababba, abbaabbaba, abbaabbaab, abbabaabab, abbabaabba, abbabababa, abbababaab, baabababab, baabababba, baababbaba, baababbaab, baabbaabab, baabbaabba, baabbababa, baabbabaab, babaababab, babaababba, babaabbaba, babaabbaab, bababaabab, bababaabba, bababababa, babababaab, abababababab, abababababba, ababababbaba, ababababbaab, abababbaabab, abababbaabba, abababbababa, abababbabaab, ababbaababab, ababbaababba, ababbaabbaba, ababbaabbaab, ababbabaabab, ababbabaabba, ababbabababa, ababbababaab, abbaabababab, abbaabababba, abbaababbaba, abbaababbaab, abbaabbaabab, abbaabbaabba, abbaabbababa, abbaabbabaab, abbabaababab, abbabaababba, abbabaabbaba, abbabaabbaab, abbababaabab, abbababaabba, abbababababa, abbabababaab, ababababababab, ababababababba, abababababbaba, abababababbaab, ababababbaabab, ababababbaabba, ababababbababa, ababababbabaab, abababbaababab, abababbaababba, ababbaabbaba, ababbaabbaab, ababbabaabab,
  4. 4. abababbabaabba, abababbabababa, abababbababaab, ababbaabababab, ababbaabababba, ababbaababbaba, ababbaababbaab, ababbaabbaabab, ababbaabbaabba, ababbaabbababa, ababbaabbabaab, ababbabaababab, ababbabaababba, ababbabaabbaba, ababbabaabbaab, ababbababaabab, ababbababaabba, ababbababababa, ababbabababaab, baabababababab, baabababababba, baababababbaba, baababababbaab, baabababbaabab, baabababbaabba, baabababbababa, baabababbabaab, baababbaababab, baababbaababba, baababbaabbaba, baababbaabbaab, baababbabaabab, baababbabaabba, baababbabababa, baababbababaab, baabbaabababab, baabbaabababba, baabbaababbaba, baabbaababbaab, baabbaabbaabab, baabbaabbaabba, baabbaabbababa, baabbaabbabaab, baabbabaababab, baabbabaababba, baabbabaabbaba, baabbabaabbaab, baabbababaabab, baabbababaabba, baabbababababa, baabbabababaab,…}  All words in S* that have seven or fewer letters: S* = { abababababab, abababababba, ababababbaba, ababababbaab, abababbaabab, abababbaabba, abababbababa, abababbabaab, ababbaababab, ababbaababba, ababbaabbaba, ababbaabbaab, ababbabaabab, ababbabaabba, ababbabababa, ababbababaab, abbaabababab, abbaabababba, abbaababbaba, abbaababbaab, abbaabbaabab, abbaabbaabba, abbaabbababa, abbaabbabaab, abbabaababab, abbabaababba, abbabaabbaba, abbabaabbaab, abbababaabab, abbababaabba, abbababababa, abbabababaab, ababababababab, ababababababba, abababababbaba, abababababbaab, ababababbaabab, ababababbaabba, ababababbababa, ababababbabaab, abababbaababab, abababbaababba, ababbaabbaba, ababbaabbaab, ababbabaabab, abababbabaabba, abababbabababa, abababbababaab, ababbaabababab, ababbaabababba, ababbaababbaba, ababbaababbaab, ababbaabbaabab, ababbaabbaabba, ababbaabbababa, ababbaabbabaab, ababbabaababab, ababbabaababba, ababbabaabbaba, ababbabaabbaab, ababbababaabab, ababbababaabba, ababbababababa, ababbabababaab, baabababababab, baabababababba, baababababbaba, baababababbaab, baabababbaabab, baabababbaabba, baabababbababa, baabababbabaab, baababbaababab, baababbaababba, baababbaabbaba, baababbaabbaab, baababbabaabab, baababbabaabba, baababbabababa, baababbababaab, baabbaabababab, baabbaabababba, baabbaababbaba, baabbaababbaab, baabbaabbaabab, baabbaabbaabba, baabbaabbababa, baabbaabbabaab, baabbabaababab, baabbabaababba, baabbabaabbaba, baabbabaabbaab, baabbababaabab, baabbababaabba, baabbababababa, baabbabababaab }
  5. 5.  No, No words can contain aaa or bbb because the first a in string ab and the a in ba never allow to make aaa or bbb.  The smallest word is of length zero (0) that is  (capital lambda) and it is present in the language so other than it there is no smallest word that is not in the language. 4. Consider the language S*, where S = {a, ab, ba}. Is the string (abbba) a word in this language? Write out all the words in this language with six or fewer letters. What is another way in which to describe the words in this language? Be careful this is not simply the language of all words without bbb. Solution:  No, the string abbba a word is not present in the language, because b individually does not exist in the given string S, so (ab b ba) can’t exist in this language.  All the words with six or fewer letters in this language are written below: S* = {, a, ab, ba, aa, aab, aba, aba, abab, abba, baa, baab, baba, aaa, aaab, aaba, aaba, aabab, aabba, abaa, abaab, ababa, abaa, abaab, ababa, ababa, ababab, ababba, abbaa, abbaab, abbaba, baaa, baaab, baaba, baaba, baabab, baabba, babaa, babaab, bababa, aaaa, aaaab, aaaba, aaaba, aaabab, aaabba, aabaa, aabaab, aababa, aabaa, aabaab, aababa, aababa, aababab, aababba, aabbaa, aabbaab, aabbaba, abaaa, abaaab, abaaba, abaaba, abaabab, abaabba, ababaa, ababaab, abababa, abaaa, abaaab, abaaba, abaaba, abaabab, abaabba, ababaa, ababaab, abababa, ababaa, ababaab, abababa, abababa, abababab, abababba, ababbaa, ababbaab, ababbaba, abbaaa, abbaaab, abbaaba, abbaaba, abbaabab, abbaabba, abbabaa, abbabaab, abbababa, baaaa, baaaab, baaaba, baaaba, baaabab, baaabba, baabaa, baabaab, baababa, baabaa, baabaab, baababa, baababa, baababab, baababba, baabbaa, baabbaab, baabbaba, babaaa, babaaab, babaaba, babaaba, babaabab, babaabba, bababaa, bababaab, babababa, aaaaa, aaaaab, aaaaba, aaaaba, aaaabab, aaaabba, aaabaa, aaabaab, aaababa, aaabaa, aaabaab, aaababa, aaababa, aaababab, aaababba, aaabbaa, aaabbaab, aaabbaba, aabaaa, aabaaab, aabaaba, aabaaba, aabaabab, aabaabba, aababaa, aababaab, aabababa, aabaaa, aabaaab, aabaaba, aabaaba, aabaabab, aabaabba, aababaa, aababaab, aabababa, aababaa, aababaab, aabababa, aabababa, aabababab, aabababba, aababbaa, aababbaab, aababbaba, aabbaaa, aabbaaab, aabbaaba, aabbaaba, aabbaabab, aabbaabba, aabbabaa, aabbabaab,
  6. 6. aabbababa, abaaaa, abaaaab, abaaaba, abaaaba, abaaabab, abaaabba, abaabaa, abaabaab, abaababa, abaabaa, abaabaab, abaababa, abaababa, abaababab, abaababba, abaabbaa, abaabbaab, abaabbaba, ababaaa, ababaaab, ababaaba, ababaaba, ababaabab, ababaabba, abababaa, abababaab, ababababa, abaaaa, abaaaab, abaaaba, abaaaba, abaaabab, abaaabba, abaabaa, abaabaab, abaababa, abaabaa, abaabaab, abaababa, abaababa, abaababab, abaababba, abaabbaa, abaabbaab, abaabbaba, ababaaa, ababaaab, ababaaba, ababaaba, ababaabab, ababaabba, abababaa, abababaab, ababababa, ababaaa, ababaaab, ababaaba, ababaaba, ababaabab, ababaabba, abababaa, abababaab, ababababa, abababaa, abababaab, ababababa, ababababa, ababababab, ababababba, abababbaa, abababbaab, abababbaba, ababbaaa, ababbaaab, ababbaaba, ababbaaba, ababbaabab, ababbaabba, ababbabaa, ababbabaab, ababbababa, abbaaaa, abbaaaab, abbaaaba, abbaaaba, abbaaabab, abbaaabba, abbaabaa, abbaabaab, abbaababa, abbaabaa, abbaabaab, abbaababa, abbaababa, abbaababab, abbaababba, abbaabbaa, abbaabbaab, abbaabbaba, abbabaaa, abbabaaab, abbabaaba, abbabaaba, abbabaabab, abbabaabba, abbababaa, abbababaab, abbabababa,…} [upto six letters]  Another way…. 5. Consider the language S*, where S = {xx, xxx}. In how many ways can x 19 be written as the product of words in S? This means: How many different factorizations are there of x 19 into xx and xxx? Solution: (xx) (xx) (xx) (xx) (xx) (xx) (xx) (xx) + (xxx) = x16 + x3 = x19 x19 can consist of 8 double xx combinations and 1 triple xxx combination i.e = 8 * 2 + 1 * 3 = 19 x19 can consist of 5 double xx combinations and 3 triples xxx combinations = 5 * 2 + 3 * 3 = 19 x19 can consist of 2 double xx combinations and 5 triples xxx combinations = 2 * 2 + 5 * 3 = 19 3 double xx combinations can be replaced by 2 triple xxx combinations like (xx)(xx)(xx) = (xxx)(xxx)

×