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NooneAtAll3today at 1:19 PM1 replyview on HN

I love SAT solver papers, always interesting to see auxiliary variable techniques, since those aren't really listed anywhere central

here for example, instead of saying {f(x,y,z)==g(x,y,z)}, authors instead make variable group a_w:=(f(x,y,z)=w||g(x,y,z)=w), and then apply "at most 1" to it. Can't be unequal if both functions only can have 1 result in total

this adds an index to iterate over, but separates internal subexpressions of f() and g(), removing 2 indixes (in this problem) and thus dropping whole power of n of clauses

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what I don't get is that they aren't searching Tarski's problem per se, but for one specific solution to it (one identity that isn't resulting from given). I'd totally look for arithmetic models that violate expectations in other ways than Wilkie


Replies

yorwbatoday at 1:53 PM

They use the properties of Wilkie's counterexample to restrict the search space. So you can't just pick arbitrary identities that hold over the positive integers and repeat the process until you've found a smaller model.