A Case for Efficient Solution Enumeration

SAT solvers have been ranked primarily by the time they take to find a solution or show that none exists. And indeed, for many problems that are reduced to SAT, finding a single solution is what matters. As a result, much less attention has been paid to the problem of efficiently generating all solutions. This paper explains why such functionality is useful. We outline an approach to automatic test case generation in which an invariant is expressed in a simple relational logic and translated to a propositional formula. Solutions found by a SAT solver are lifted back to the relational domain and reified as test cases. In unit testing of object-oriented programs, for example, the invariant constrains the representation of an object; the test cases are then objects on which to invoke a method under test. Experimental results demonstrate that, despite the lack of attention to this problem, current SAT solvers still provide a feasible solution. In this context, symmetry breaking plays a significant, but different role from its conventional one. Rather than reducing the time to finding the first solution, it reduces the number of solutions generated, and improves the quality of the test suite.