Theories of computability
Complexity classifications of boolean constraint satisfaction problems
Complexity classifications of boolean constraint satisfaction problems
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
The complexity of satisfiability problems: refining Schaefer's theorem
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
What makes propositional abduction tractable
Artificial Intelligence
Structure identification of Boolean relations and plain bases for co-clones
Journal of Computer and System Sciences
The expressive power of valued constraints: Hierarchies and collapses
Theoretical Computer Science
The complexity of satisfiability problems: Refining Schaefer's theorem
Journal of Computer and System Sciences
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The complexity of various problems in connection with Boolean constraints, like, for example, quantified Boolean constraint satisfaction, have been studied recently. Depending on what types of constraints may be used, the complexity of such problems varies. A very interesting observation of the recent past has been that the thus derived classification of constraints can be explained with the help of universal algebra. More precisely, the difficulty of such a constraint problem often depends on the co-clone the constraints are from. A co-clone is a set of Boolean relations that is closed under very natural closure operations. Nearly all these co-clones can be generated by said operators out of a finite set of relations, a so-called base. Knowing a, preferably simple, base for each co-clone can therefore be of great value when studying the complexity of Boolean constraint problems, since this knowledge reduces the infinitely many cases of equivalent problems to a single one--the constraint satisfaction problem for this base. In this paper we give a finite and simple base for every Boolean co-clone, where this is possible. We give evidence that the presented bases are as easy as possible.