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Can anyone explain each option in detail. I am unable to get this property. .!!

in Theory of Computation 2.4k views

1 Answer

15 votes
Let L={0,10,110,1111} . this language satisfies the prefix property since a string in this language will not act as prefix for other strings in this language. Consider another language L1={01,11,110,011}. In this language 01 is acting as a prefix for 011 and 11 is acting as a prefix for 110. Therefore this is not a language satisfying prefix property.

Just have a look at option d.

Language contains strings over (0+1)* where number of 0's = number of 1's

consider 2 strings 01,0110 in the language. 01 is a prefix for 0110. So this language does not satisfy prefix property.

Other three languages satisfy prefix property.
0
Thnku for this explanation.. I got it now.
1
i think $B$ too will not followprefix property because $B=(a+b)^{*}$
1
I think you are considering x as (0+1)* . x is just one character here.

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