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pairwise disjointness test

Posted on 2010-11-13
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Last Modified: 2012-05-10
I need to know how to Perform the pairwise disjointness test for the following grammar rules and say if they pass the test or fail the test


A)    A-->aB | b | cBB

B )   B-->aB |bA |aBb

C-)  C-->aaA |b|caB

need correct information
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Question by:SweetsJamRock
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Kendor earned 1000 total points
ID: 34127031
looks like homework. but let me help you out a bit...

remember what you are looking for "two sets A and B are disjoint if their intersection is the empty set" meaning that no Element of set A occurs in set B and vice-versa. Now you have more than two sets, then the definition extends. A collection of sets is pairwise disjoint if any two sets in the collection are disjoint.

look at A):
you have three sets. set 1: aB, set 2: b, set 3: cBB
compare set1 and set 2: do they intersect (do they have same elements)? compare set 1 and set 3: do they intersect? compare set 2 and set 3: do they intersect?

now is the collection of A) pairwise disjoint? (did you answer any of the above comparisons with "no"?)

continue with B and C
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by:Kendor
ID: 34127039
ah - I just realized that these are not 3 different tasks A,B, C, right? these are collections?
then things change slightly... you then compare the collections AB AC and BC...
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Author Closing Comment

by:SweetsJamRock
ID: 34202251
you have partially gotten the concept right, even though your solution have many flaws.

i will award you some points for your assistance
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