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I was wondering if, given an algorithm for 3SAT, testing it on Barthel instances would provide a general idea of how well it empirically performs on hard instances. What would other hard instances look like that would perhaps be more telling?

Defining Barthel instances: I have only seen them namedropped so I thought they were a thing. I could only find nothing else than this paper: https://arxiv.org/abs/cond-mat/0111153, which says they are physics inspired instances of "hard and satisfiable instances" for 3SAT. After that I don't know because I don't know what a ferromagnetic phase or a glassy excited state is. The paper is kinda old too from 2001.

Würthi
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  • Factoring coprimes make really hard SAT problems too. You'd need to write code to generate the SAT using the method for multipling binary numbers to create the boolean expressions. But there might be some online generators to save time. – clinux Jul 07 '22 at 00:22
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    You can look at recent SAT competitions for inspiration. There are hard graph coloring instances too, by the way. – Juho Jul 07 '22 at 19:13

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