2 votes 2 votes For a regular expression $e$, let $L(e)$ be the language generated by $e$. If $e$ is an expression that has no Kleene star $\ast$ occurring in it, which of the following is true about $e$ in general? $L(e)$ is empty $L(e)$ is finite Complement of $L(e)$ is empty Both $L(e)$ and its complement are infinite Theory of Computation cmi2016 regular-language regular-expression closure-property + – go_editor asked Dec 30, 2016 recategorized Nov 8, 2019 by Lakshman Bhaiya go_editor 817 views answer comment Share Follow See all 4 Comments See all 4 4 Comments reply Overflow04 commented Nov 11, 2022 reply Follow Share @Kabir5454 what if e itself is ε 0 votes 0 votes Kabir5454 commented Nov 11, 2022 reply Follow Share What are you implying? 0 votes 0 votes Overflow04 commented Nov 11, 2022 reply Follow Share @Kabir5454 Given: let L(e) be the language generated by e. e can be 0 +1 or 0+00 or any other thing does e = ε possible. 0 votes 0 votes Kabir5454 commented Nov 12, 2022 reply Follow Share yes why not . $L(e)=\left \{ \epsilon \right \}$. The corresponding regular expression is = $\epsilon$ . Here $L(e)$ is not empty but finite with a string of $0$ length . Complement of $L(e)$=$(a+b)^{+}$ assuming $\sum =\left \{ a,b \right \}$ which is infinite not empty . so option C is also false . Option D is also false as $L(e)$ is finite . 1 votes 1 votes Please log in or register to add a comment.
1 votes 1 votes Suppose R.E $e = 00 + 11$ Language generated by R.E is $L(e) = \left \{ {00,11}\right \}$ Clearly the given language is finite So option B. complement of L is $\Sigma ^*- \left \{ {00,11}\right \}$ not empty. Prabhanjan_1 answered Dec 30, 2016 Prabhanjan_1 comment Share Follow See all 5 Comments See all 5 5 Comments reply Show 2 previous comments Tesla! commented Apr 28, 2018 reply Follow Share let me put in this way consider DFA with 2 states q0 and q1 where q0 is finial and q1 is final and let $\Sigma$={a} a $\rightarrow$q0 q1 *q1 q1 now tell me is given DFA valid for this question 0 votes 0 votes abhishekmehta4u commented Apr 28, 2018 reply Follow Share your dfa contain kleene star 00* 0 votes 0 votes Tesla! commented Apr 28, 2018 reply Follow Share so what you are trying to say that by any means we should not be able to generate 0+ directly or indirectly 0 votes 0 votes Please log in or register to add a comment.
0 votes 0 votes Answer: soujanyareddy13 answered May 6, 2021 soujanyareddy13 comment Share Follow See all 0 reply Please log in or register to add a comment.