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Assignment4 q3

Posted by giggs 
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Assignment4 q3
July 19, 2007 01:18PM
Did anyone manage to prove the equivalent? coz i got two FA's that do not accept anything and the other one accept null... i'm a lost???
Anonymous User
Re: Assignment4 q3
July 19, 2007 01:29PM
To test for equivalence between the two FA's, set them out in the formula below and evaluate them in a boolean fashion:
(FA1' + FA2)' + (FA2' + FA1)'
Re: Assignment4 q3
July 19, 2007 01:44PM
I used the same formula, and (FA1'+FA2)' gives NULL
and (FA1' + FA2)' gives nothing

but in this case if one accept NULL and the other except empty string, the two are not equivalent.
Did u get an empty string in both (FA1'+FA2)' and (FA1' + FA2)' ??
Anonymous User
Re: Assignment4 q3
July 19, 2007 02:11PM
I worked out each FA and it's complement (drew 4 FA's). Then I drew each bracketed expression and it's complement (another 4 FA's). I was then in a position to evaluate my expression. It evaluated to TRUE and so I said my FA's were equivalent.
avatar Re: Assignment4 q3
July 19, 2007 02:15PM
If the language (L1’ + L2)’ + (L2’ + L1)’ is empty, then the two FAs is equivalent. If the language is not emptly, then the two FAs is not equivalent.
For (FA1’ + FA2) there are three final stages and for (FA1’ + FA2)‘ there is a final state. When combined with (FA2’ + FA1)’, the new combined FA would also have a finale state. So, there will be words that could be accepted by the machine and thus the language is not empty.
Therefore, the given FA1 and FA2, are not equivalent.
Anonymous User
Re: Assignment4 q3
July 19, 2007 02:24PM
Reanie Wrote:
-------------------------------------------------------
> If the language (L1’ + L2)’ + (L2’ + L1)’
> is empty, then the two FAs is equivalent.

I think I missed that part in the book? That doesn't make sense to me. Is there some proof of this?
Re: Assignment4 q3
July 19, 2007 02:25PM
OHHH!!! just got now, Please check the end of question 5, it states "Why is this problem wrong? How can it be fixed?"
avatar Re: Assignment4 q3
July 19, 2007 02:29PM
I didn't answer the last part of the question, wanted to but forgot about it.
Anonymous User
Re: Assignment4 q3
July 19, 2007 02:30PM
Ja, I said that there is an unnecessary circuit formed in FA1. The b edge returning to the start state should be looped onto the state from where it originates.
avatar Re: Assignment4 q3
July 19, 2007 02:33PM
Rick Wrote:
-------------------------------------------------------
> Reanie Wrote:
> --------------------------------------------------
> I think I missed that part in the book? That
> doesn't make sense to me. Is there some proof of
> this?

Rick, I've sent you an email. I'll check the correct proof tonight and post it here.
Re: Assignment4 q3
July 19, 2007 02:41PM
Reanie Wrote:
-------------------------------------------------------
> If the language (L1’ + L2)’ + (L2’ + L1)’
> is empty, then the two FAs is equivalent. If the
> language is not emptly, then the two FAs is not
> equivalent.
> For (FA1’ + FA2) there are three final stages
> and for (FA1’ + FA2)‘ there is a final state.
> When combined with (FA2’ + FA1)’, the new
> combined FA would also have a finale state. So,
> there will be words that could be accepted by the
> machine and thus the language is not empty.
> Therefore, the given FA1 and FA2, are not
> equivalent.

Thanks Reanie... and u guys 4 the feed back. Rick, i hope u also got something...
avatar Re: Assignment4 q3
July 19, 2007 02:47PM
I'm repeating this subject, so I have last year's tut's as examples. Not all my thinking.
avatar Re: Assignment4 q3
July 19, 2007 03:21PM
I've downloaded the study guide from MyUnisa - the Afr version, but the pages should be more-or-less the same.
On p71-72 Chp 11 are being described and how to do the sums.
On p133-141 examps have been worked out. Especially ex 6 is the same scenario as (I think) we had.
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