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| '''Example:''' x <FONT FACE="Symbol">Î</FONT> {c1, ..., cl} is equivalent to the discution of l constraints x=c1, ..., x=cl. | '''Example:''' see attachment:LinDecompEx1.pdf |
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Needs updating
I do not have a general definition. I suspect that if something is linearly decomposable that it can be written as a set of linear equations.
Unary Constraint Domains
Unary constraint domains are linearly decomposable if there exists a constant d such that, given any set C of BasicConstraints about one variable x, there exists a set C' of basic constraints about x such that |C'| <= d|C|, where |C| is the sum of the sizes of constraints in C for some appropriate notion of size (e.g. number of symbols in a constraint), and the conjunction of any subset of C union C' is a decomposition of C.
What this means is that given a set of basic constraints there is a finite set of constraints that we can union to our original set so that any subset of the conjuction of C and C' can be writen as a disjunction of C' alone.
Example: see attachment:LinDecompEx1.pdf
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