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NP completeness of closest vector problem
There is a mismatch in terminology in your question. The problem you specify is known as the shortest vector problem (SVP). You called it the closest vector problem (CVP), but the CVP is something ...

D.W.♦
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Are there any open source SAT solvers with UNSAT core extraction algorithm built in?
Minisat and Z3 have the same hack to extract unsat cores. I found the Z3 example easy to understand. The link is here:
https://github.com/Z3Prover/z3/blob/master/examples/c%2B%2B/example.cpp
There are ...
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