# what does it mean to extend an assignment?

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

## 1 Answer

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.