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From: puget@ilog.ilog.fr (Jean-Francois Puget)
Subject: Re: [Q] Modularity in Constraint Management Approaches?
Message-ID: <1995Jun20.115528.10504@ilog.fr>
To: Nenad Ivezic <ni10+@andrew.cmu.edu>
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References:  <UjtS4QG00YUv8xkltX@andrew.cmu.edu>
Date: Tue, 20 Jun 95 11:55:28 GMT
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In article <UjtS4QG00YUv8xkltX@andrew.cmu.edu>, Nenad Ivezic <ni10+@andrew.cmu.edu> writes:
|> Hi,
|> 
|> I need your feedback on an intuition that may be plain wrong or long
|> known or ...  At any rate, if this intuition is correct, I would appreciate
|> any pointer to the work that has addressed it from a theoretical and
|> practical aspects.  And, yes, I am knew to constraint management arena, so
|> bare with me, please.
|> 
|> Here is the intuition:
|> 
|>   Suppose that we have a unique space of decision variables, say D.
|>   Further suppose that there exist two (or more for that matter) collections
|>   of constraints imposed on the space of decision variables, say C1 and C2.
|>   Finally, let two computational approaches be applied to the two sets of
|>   constraint collections, C1 and C2.  Call these approaches A1 and A2.
|> 
|>   My conjecture is that if application of A1 and A2 on C1 and C2 results
|>   in solutions (i.e., decision variable values ranges) D1 and D2, then
|>   the resulting solution of applying  C1 and C2 simultaneously would be
|>   C1 intersection C2.
|> 
|> A note: A1 is applied on C1 independently from A2 applied on C2.
|> 
|> Any takers?
|> 

I am not sure to have understood your question clearly, but here is a counter
example to one possible interpretation of the question.

Take C1 : x < y

Take C2 : y < x

Start with x in [0, 10]
           y in [0, 10]
x and y integers

Assume arc-consistency is used as computational approach.

Then D1 is x in [0,  9]
           y in [1, 10]

 and D2 is x in [1, 10]
           y in [0,  9]

D1 intersection with D2 is
           x in [1,  9]
           y in [1,  9]

which is not what would be obtained by stating both constraints
x < y and y < x and applying arc consistency. In this case, a 
contradiction is detected (domains become empty).


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  Jean-Francois Puget		 net : puget@ilog.fr
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