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Hey can you help me in this assignment, it is in attach file

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Assignment 2, COSC 4P61, Theory of Computation, Fall, 2016 Due: Oct. 25, Tuesday, 5:00 PM. 1. (25) Find DFAs (draw their state transition diagrams) that accept the following languages: (a) The set of strings over { a, b } where every a is immediately followed by a b ; (b) The set of strings over { a, b, c } that do not contain the substring aaa ;. (c) The set of strings over { a, b, c } that begin with a , contain exactly two b ’s, and end with cc ; (d) The set of binary strings (encodings), without leading 0’s, of natural numbers that are divisible by 4. (e) ( ab ) * ( ba ) * ; 2. (15) Consider the following NFA without e -moves: (1) give a regular expression for the language accepted; (2) Convert it to a DFA using the standard algorithm described in class. Please also draw the state transition diagram. δ ( q 0 , a ) = { q 1 , q 2 } δ ( q 1 , a ) = { q 1 } δ ( q 1 , b ) = { q 0 , q 1 } δ ( q 1 , c ) = { q 1 } δ ( q 2 , a ) = { q 2 } δ ( q 2 , b ) = { q 2 } δ ( q 2 , c ) = { q 0 , q 2 } 3. (20) Give examples of languages L 1 and L 2 over { a, b } that satisfy the descriptions below: (a) L 1 is regular, L 2 is nonregular, and L 1 u L 2 is regular; (b) L 1 is regular, L 2 is nonregular, and L 1 u L 2 is nonregular; (c) L 1 is regular, L 2 is nonregular, and L 1 i L 2 is regular; (d) L 1 is nonregular, L 2 is nonregular, and L 1 u L 2 is regular. (e) L 1 is nonregular, L 2 is nonregular, and L 1 i L 2 is regular. 4. (15) Prove or disprove the following: (a) If L * is regular, then L must be regular. (b) For any language L , L * must be regular. (c) If L 1 L 2 is regular, then both L 1 and L 2 have to be regular. (d) The union of ±nite number of regular languages is always regular. (e) The union of in±nite number of regular languages is always regular. 5. (25) Use the Pumping Lemma to show that the following languages are not regular. (a) { a i b j | i > j } (b) { a p a q | for all intEgErs p and q whErE q is a primE numbEr and p is not primE } . (c) { a i b j || i - j | = 3 } (d) { a i b j c k | i = j or j n = k } (e) { a i b j | i/j is an intEgEr } 1
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25, Tuesday, 5:00 PM. (25) Find DFAs (draw their state transition diagrams) that accept the following languages: (a) The set of strings over {a, b}...
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