Hardness of Solving Relational Equations

Minimal solutions play a crucial role in describing all solutions of relational equations. For this reason, the problem of computing minimal solutions has for long been examined. The literature contains several algorithms for computing minimal solutions. Recently, contributions regarding computational complexity of the problem itself appeared. The complexity aspect is clearly of fundamental importance. However, the existing results contain serious flaws. In this paper, we inspect the existing contributions, clarify the flaws, examine the problem of complexity of computing minimal solutions, prove that there is no efficient algorithm computing all minimal solutions, and discuss further ramifications of our observations.