Question 5: CFGa. Make a CFG for the language a3nbm(aba)2mbn, where n,m>0b. Make a DFA that accepts all words that start with 'aab', and then convert the DFA to a CFG usingthe simple procedure we did in class.

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Answered: a. Make a CFG for the language…

Computer Networking: A Top-Down Approach (7th Edition)

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Chapter1: Computer Networks And The Internet

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Problem R1RQ: What is the difference between a host and an end system? List several different types of end...

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Let Σ be a non-empty alphabet and LCE* be a context-free language. Which of the following languages is/are necessarily context-free? Note: For some string w = Σ*, w is the string reversal. € 1. reverse_1(L) = {xy : ³x, y ≤ Σ*, x € L and yR € L} R 2. reverse_2(L) = {x : 3x € Σ*, x € L and x² EL If a language is necessarily context-free, prove your claim. Any construction you make does not require a proof of correctness. If a language is not necessarily context-free, give a counterexample language L which is context- free but for which reverse_i(L) (i 1, 2) is not context-free. To do so, you must show that your language L is context-free by giving either a PDA which accepts it or a CFG which generates it. You do not need to prove the correctness of your construction but you should explain how it works. In addition, you must give a Pumping lemma proof which shows that reverse; (L) is not context-free. =
b) Write the CFG for the following language over alphabet Σ= {p,q ,r} L={ pqr, ppqrr, pppqrrr, ppppqrrrr, pppppqrrrrr, ……………..} Hint : pn q rn where n>=1 Note: derive at least four strings for the given CFG
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Build a TM to accept the language of all words of a's and b's that contain at least one aa or one bb. For example, ababba, bababaa, bababaabb are accepted, but ababab and bababab are not accepted.
2. Draw the DFA for the following languages a. L = {w|w contains substring “aba" and has b in the second last position} b. L = {w[ every 3rd symbol in w is 0} e.g. 110100, 000110001. But 101 won't be accepted since the 3rd symbol is 1. c. Set of all strings that are at least of length 4 and contain an even number of 1's d. L = {w| The 3rd last symbol in w is 0}
Let L1, L2, and L3 be languages over some alphabet. In each case below, two languages are given. Say what the relationship is between them. (Are they always equal? If not, is one always a subset of the other?) Give reasons for your answers, including counterexamples if appropriate. 1. L1(L20L3), L1L20LL3 2. LinL;, (L nL2)*
Write a regular expression representing the following language over the alphabet {0,1}. Language of all strings that do not have 2 consecutive 1s.
Question 2 c) Give a regular expression for the following regular languages, assuming the alphabet is Σ := {0, 1}. I. The set of all strings, when viewed as binary representation of integers, that are divisible by 2. II. The set of all strings containing 00. III. Give a closed-form regular expression for the set of all string not containing consecutive 00.
Construct a CFG and PDA for the language B={w| w is a string over {a,b} with the same count of a's and b's}. For example, abba € B, abab e B,aabb € B, babbbaaaba € B, that is, there is no particular order in which a's and b's appear in w as long as there is the same amount of them.
Construct a PDA that matches all strings in the language over {x,y} such that each string has an odd length and its middle symbol is 'x'. Editor Below, give a short description of the set of strings associated with each state of your PDA.

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a. Make a CFG for the language a3nbm(aba)2mbn, where n,m>0 b. Make a DFA that accepts all words that start with 'aab', and then convert the DFA to a CFG using the simple procedure we did in class.