Let = {0, 1}. Consider the following languages over Σ.L1 {w every second letter of w is 0}L2 = {w every third letter of w is 1}:(a) Write down a length 5 string that is in L1 L2.(b) Give the state diagram for a DFA that recognizes L1.(c) Give the state diagram for a DFA that recognizes L2.(d) Give the state diagram for a DFA that recognizes L1 L2.

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Answered: Let = {0, 1}. Consider the following…

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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Draw the state diagram
Consider the language over the alphabet Σ = {0, 1} containing strings which include nonempty binaries(strings with 0’s and 1’s) that start with 1 and end with 0 and have at least three digits. For example, 110and 1100 are such binaries, while 10 and 010 are not.1. Write a regular expression for this language 2. Draw a DFA diagram for this language, with no more than six states. 3. Is the language regular? Why or why not?
Q5. Let XDFA = {(A)| A is a DFA and L(A) is an infinite language}. Show that XDFA is decidable.
A palindrome is a string that reads the same backward as forward, i.e., w = wR. A palindromic language is one in which all the strings are palindromes, i.e., some subset of P = {w | w ∈ Σ∗ and w = wR} Consider the language L ={<B> | B is a DFA with input alphabet Σ and L(B) contains a palindrome}. Show that L is decidable. Explain step by step.
Draw DFAs for the following language specifications. 1. All strings on Σ ={A, B, C} that contain each letter (A, B, and C) at least once. 2. All strings on Σ ={X,Y, Z} that contains two consecutive Xs or three consecutive Zs (or both). 3. All strings on Σ ={A,B,C,D that match the Python regular expression ^(A?(B|CD)*A+D)$
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. =
Theory of autometa
Let L, and L2 be the languages defined as follows: L1 ={ xe{0,1}* | x has an odd number of Os}. L2 ={ 0"1m0" | n, m 20} Which of the following context-free grammars generates the language L1 U L2? (Here all uppercase letters are variables) O E- 1E| OF F- 1F| OE je A- OAO | B B - 1B|E OS-E|A E - OF | 1E F- OE | 1F|E A- OAO | 1A|E OS- S1 | S2 S1 → 00S | 15 | 01A| 10A | B A- 10S | 01S B-1|8 S2→ OS,0| A2 A2 - 1| S2|E S-E|A E- 1E| OF F- 1F| OE je A- OAO | B B- 1B|E
Consider the language over the alphabet Σ = {0, 1} containing strings which include nonempty binaries(strings with 0’s and 1’s) that start with 1 and end with 0 and have at least three digits. For example, 110and 1100 are such binaries, while 10 and 010 are not.1. Write a regular expression for this language 2. Draw a DFA diagram for this language, with no more than six states. 3. Is the language regular? Why or why not?
Q No. 3: Grammar G1 = ( N = { E, T, F, I, D}, T = { +, *, (, ), 0-9}, S = {E} and P is the set of productions: E E +T | T T T * F | F E) | I DI | D F I D + 0|1|2|3|4 |5 | 6 | 7 | 8 |9 For the string w = (9*(9+9)+999), find- 1. Leftmost derivation 2. Rightmost derivation 3. Parse Tree
Formal Languages and Automata Questions
Assignment 1. Design Push Down Automata for the following language, Consider E= {a,b} L= {w | w is a string of (a,b)* where number of 'a' and number of 'b' is not equal} Hints: The string can contain 'a andb' in any combination (star * operation). But the number of 'a' and 'b' will be unequal in the accepted string. Some example strings: aabbababa, bbbaabaabbbb, bababababab, aaaaaaaba etc.

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