Generalizations of Watched Literals for Backtracking Search

The technique of watching two literals per clause to determine when a clause becomes a unit clause was introduced recently in the Chaff satisfiability program. That program does not perform either equivalent-literal detection or binary-clause detection. We describe a generalization of the technique that handles the tracking necessary to support equivalent-literal detection and binary-clause detection. Both generalizations are designed to preserve the important property of the original method that unbinding a variable is very efficient. We decribe a data-structure technique called “lazy deletion” that permits several operations to be performed in amortized constant time, where the more straightforward implementation might require linear time per operation. The overall efficiency of generalized technique is analyzed. Preliminary implementation results are reported.