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Is there a way to change the satisfiability of a SAT problem without knowing whether the original problem is satisfiable or not beforehand?

There are satisfiability-preserving operations like removing supersets or resolution that maintain the satisfiability status of a problem independent of its label. Is there a way to do the opposite?

Maria S.
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  • I doubt this is possible. You can easily turn a known SAT/UNSAT to other way around, but I suspect "flipping" is going to be just as hard as solving the satisfiability problem itself. (i.e., any solution, if exists, will be exponential in the size of the formula at best.) – alias Jan 25 '22 at 16:28
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    I mean, there are some trivial solutions depending on what you mean by "change". You can make it sat by removing all the clauses, and you can make it unsat by adding them all. But that's probably not what you intend - what operations are you looking to perform? – GManNickG Jan 25 '22 at 21:17
  • @GManNickG Excellent point! While it's impossible to know what the OP intended, I interpreted as by doing as "minimal" a change as possible. (Adding/removing the fewest clauses, for instance.) Admittedly, what "minimal" means will play an essential role. In any case, your comment should be the answer. – alias Jan 28 '22 at 07:37

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