A Boolean Encoding Including SAT and n-ary CSPs

We investigate in this work a generalization of the known CNF representation which allows an efficient Boolean encoding for n-ary CSPs. We show that the space complexity of the Boolean encoding is identical to the one of the classical CSP representation and introduce a new inference rule whose application until saturation achieves arc-consistency in a linear time complexity for n-ary CSPs expressed in the Boolean encoding. Two enumerative methods for the Boolean encoding are studied: the first one (equivalent to MAC in CSPs) maintains full arc-consistency on each node of the search tree while the second (equivalent to FC in CSPs) performs partial arc-consistency on each node. Both methods are experimented and compared on some instances of the Ramsey problem and randomly generated 3-ary CSPs and promising results are obtained.