CS 390 Solutions to Homework 9



Textbook pp. 194 - 195:

5.20 (a) To distinguish tex2html_wrap_inline71 and tex2html_wrap_inline73 , tex2html_wrap_inline75 , append tex2html_wrap_inline77 . Then tex2html_wrap_inline79 but tex2html_wrap_inline81 .

5.26 (a) No. Let tex2html_wrap_inline103 and tex2html_wrap_inline105 .
(c) No. Let tex2html_wrap_inline103 and tex2html_wrap_inline109 . Then tex2html_wrap_inline111 is regular but neither tex2html_wrap_inline113 nor tex2html_wrap_inline115 is regular.
(g) Yes. Since   L1 L2   is regular,   L1 - L2 = L1 - ( L1 L2)   is regular. Now L2 = ( L1 L2 ) - ( L1 L2 ). Hence if   L1 L2   is regular, L2 is regular, since the difference of regular languages is regular.

5.27 (c) Let tex2html_wrap_inline127 be the infinite set. Then tex2html_wrap_inline129 and tex2html_wrap_inline131 for tex2html_wrap_inline133 can be distinguished with respect to the language in question by appending tex2html_wrap_inline135 to them (0 is in the middle for tex2html_wrap_inline129 but not for tex2html_wrap_inline131 ). Therefore the language is not regular.