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HM4-FSMsAndRegEXs-Ch7-Closure

# HM4-FSMsAndRegEXs-Ch7-Closure - a pref L = w 5 x ∈ Σ wx...

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CS 341 Automata Theory Elaine Rich Homework 4 Due: Thursday, February 8, 2007 1) Consider the following FSM M : a a b 1 b 2 a 3 b 4 a,b a) Show a regular expression for L ( M ). b) Describe L ( M ) in English. 2) Consider the following FSM M : q 0 a q 1 b q 3 b a b q 2 a) Write a regular expression that describes L ( M ). b) Show a DFSM that accepts ¬ L ( M ). 3) Show a regular grammar for each of the following languages: a) { w { a , b }* : w does not end in aa }. b) { w { a , b }* : w does not contain the substring aabb }. 4) Consider the following regular grammar G : S a T T b T T a T a W W ε W a T a) Write a regular expression that generates L ( G ). b) Use grammartofsm to generate an FSM M that accepts L ( G ). 5) Prove by construction that the regular languages are closed under: a) intersection. b) set difference. 6) Prove that the regular languages are closed under each of the following operations:

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Unformatted text preview: a) pref ( L ) = { w : 5 x ∈ Σ * ( wx ∈ L )}. b) suff ( L ) = { w : 5 x ∈ Σ * ( xw ∈ L )}. c) reverse(L) = { x ∈ Σ * : x = w R for some w ∈ L }. d) letter substitution (as defined in Section 8.3). 7) Using the definitions of maxstring and mix given in Section 8.6, give a precise definition of each of the following languages: a) maxstring (A n B n ). b) maxstring ( a i b j c k , 1 ≤ k ≤ j ≤ i ). c) maxstring ( L 1 L 2 ), where L 1 = { w ∈ { a , b }* : w contains exactly one a } and L 2 = { a }. d) mix (( aba )*). e) mix ( a * b *)....
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HM4-FSMsAndRegEXs-Ch7-Closure - a pref L = w 5 x ∈ Σ wx...

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