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Given a generic K-SAT instance $S$ with $n$ boolean variables.

Is it possible to convert a clause of this instance into an equivalent p-in-L SAT system of equations such that the number of new clauses introduced is more than the number of new variables introduced?

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  • $\begingroup$ I think this answer provides such a reduction. cstheory.stackexchange.com/a/42223/45276 $\endgroup$
    – rus9384
    Commented Feb 25 at 18:02
  • $\begingroup$ @rus9384 Thank you. But the $(x, x', F_1)$ and $(\neg x, \neg x', F_1)$ is essentially introducing a dummy variable $(F_1)$ that will always have to be FALSE and I am trying to avoid such tricks (dummy variables and clauses)... $\endgroup$ Commented Feb 25 at 18:38

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