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(Solved) : 19 12 Points Let B 040 12 1 R E Show B2 Regular B Wrong Following Argument Assume B2 Reg Q28959347 . . .

19. (12 points). Let B,-(040 12 1,r E Σ*). a) Show that B2 is regular. b) What is wrong with the following argument: Assume B2 is regular, and let m be given. Consider the string010m e B2 and decompose w = xyz with r e, y = 0. and z = 10. Then, setting i = 0 yields a string tro = rys-xy: = 10 which is not in B2-Hence, by the pumping lemma, we have a contradiction. We conclude that B2 is not regular19. (12 points). Let B,-(040 12 1,r E Σ*). a) Show that B2 is regular. b) What is wrong with the following argument: Assume B2 is regular, and let m be given. Consider the string010m e B2 and decompose w = xyz with r e, y = 0″. and z = 10″. Then, setting i = 0 yields a string tro = ry’s-xy”: = 10″ which is not in B2-Hence, by the pumping lemma, we have a contradiction. We conclude that B2 is not regular Show transcribed image text

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