Hardness of Solving Relational Equations


Minimal solutions play an important 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 many algorithms for computing minimal solutions. Recently, contributions concerning computational complexity of the matter itself appeared. The complexity facet is clearly of elementary importance. But, the present results contain serious flaws. During this paper, we inspect the present contributions, clarify the issues, examine the problem of complexity of computing minimal solutions, prove that there's no efficient algorithm computing all minimal solutions, and discuss any ramifications of our observations.

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