For a constraint satisfaction problem, what does it mean for an assignment x to extend an assignment a?

Sorry if this is super trivial, I did not find an answer

e.g here: No Small Linear Program Approximates Vertex Cover Within a Factor 2 − $ \epsilon $ pg 16 x does not extend \alpha


It means that you have a partial solution, and you extend that partial solution by assigning at least one more variable to some value, thus producing either a new partial solution or a solution where every variable is assigned a value.

Put differently, if $x$ extends an assignment $a$, it holds that $x$ does precisely the same assignments as $a$ and assigns any number of other variables in addition.


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