Canonical Computation without Canonical Representation

A representation of a Boolean function is canonical if, given a variable order, only one instance of the representation is possible for the function. A computation is canonical if the result depends only on the Boolean function and a variable order, and does not depend on how the function is represented and how the computation is implemented. In the context of Boolean satisfiability (SAT), canonicity of the computation implies that the result (a satisfying assignment for satisfiable instances and an abstraction of the unsat core for unsatisfiable instances) does not depend on the functional representation and the SAT solver used. This paper shows that SAT-based computations can be made canonical, even though the SAT solver is not using a canonical data structure. This brings advantages in EDA applications, such as irredundant sum of product (ISOP) computation, counter-example minimization, etc, where the uniqueness of solutions and/or improved quality of results justify a runtime overhead.