Problem Detail: I have to make a regular expression from the following laguage:
{$a^kb^mc^n : $ where k + m + n is odd}
Is is possible for the sum of three numbers to be odd (other than three consecutive odd numbers)? I have this so far:
{(abbbccccc) + (abbbbbccc) + (aaabccccc) + (aaabbbbbc) + (aaaaabccc) + (aaaaabbbc)}
but I am realizing that there are way more possibilities to this pattern… How can I formulate a string that encompasses all of this?
Asked By : jsan
Answered By : vonbrand
What you need is that either exactly two of $k$, $m$, $n$ even, or all three odd, because two odds and an even make an even; and three evens make an even. An odd number of $a$’s translates to the regular expression $a (a a)^*$, an even number to $(a a)^*$. Pulling the above together: $$ a (a a)^* (b b)^* (c c)^* mid (a a)^* b (b b)^* (c c)^* mid (a a )^* (b b)^* c (c c)^* mid a (a a)^* b (b b)^* c (c c)^* $$
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Question Source : http://cs.stackexchange.com/questions/9478
