Ullman (TOC) Edition 3 Exercise 3.1 Question 2 (Page No. 91)

Question

Write regular expressions for the following languages$:$

1. The set of all strings of $0's$ and $1's$ such that every pair of adjacent $0's$ appears before any pair of adjacent $1's.$
2. The set of strings of $0's$ and $1's$ whose number of $0's$ is divisible by five.

Answer 1

for part a go to this link

https://cs.stackexchange.com/questions/34025/regex-any-pair-of-zeros-is-before-any-pair-of-ones

for part b REX will be (1*01*01*01*01*0)* +1*

Comments

What about 1, 11, 111... ?? The number of 0s is divisible by 5 but it's not accepted by the regex. I think $(1^{*}01^{*}01^{*}01^{*}01^{*}0)^{*}1^{*}$ will be more appropriate

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this regex is not correct as this will generate exactly 5 zeros only.

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It was a typo. Your original answer didn’t include 1*. That was my query. Seems like you’ve corrected it 👍

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yes i missed 1* in my original answer so edited now.