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Is this problem NP-complete?

I have many restrictions like this and want to find a feasible solution:

((a and b) xor (c and d)) = 1

with a,b,c,d are arbitrary literals. It looks similar to XOR-2SAT but has additional ANDs inside the clause.

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  • $\begingroup$ Are the ANDs mostly of 2 literals? ​ ​ $\endgroup$ – user12859 Sep 19 '16 at 14:41
  • $\begingroup$ yes they are!!! $\endgroup$ – guest1000 Sep 19 '16 at 14:47
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    $\begingroup$ Welcome to CS.SE! Can you be more precise? Do all and-clauses have exactly 2 literals? are literals always in positive form, or could they be negated? Are the xor's always of exactly 2 and-clauses? Can you edit the question accordingly? $\endgroup$ – D.W. Sep 19 '16 at 16:19
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Your question is likely answered by Schaefer's dichotomy theorem. In particular, if an instance of your problem is a conjunction of formulas, each one depending on a bounded number of variables, then according to the theorem your problem is either in P or NP-complete; and moreover there is a simple criterion to decide which case it is.

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