11. The system of claim 8 , wherein to generate an undirected equivalence graph in the plurality of the undirected equivalence graphs, the processor is further configured to: generate a first node and a second node, wherein the first node corresponds to a first table and a set of attributes and the second node corresponds to a second table and a set of attributes, wherein the first table, the second table and the attributes are included in an equivalence class in the plurality of equivalence classes; generate an edge between the first node and the second node; and annotate the edge with a second predicate referencing the attribute between the first node and the second node; wherein the second predicate is a component of the query predicate.
11. The system of claim 8 , wherein to generate an undirected equivalence graph in the plurality of the undirected equivalence graphs, the processor is further configured to: generate a first node and a second node, wherein the first node corresponds to a first table and a set of attributes and the second node corresponds to a second table and a set of attributes, wherein the first table, the second table and the attributes are included in an equivalence class in the plurality of equivalence classes; generate an edge between the first node and the second node; and annotate the edge with a second predicate referencing the attribute between the first node and the second node; wherein the second predicate is a component of the query predicate. 12. The system of claim 11 , to generate the undirected equivalence graph, the processor is further configured to: generate a third node including a constant vector; generate a second edge between a first node and a third node; and annotate the second edge with a third predicate referencing the attributes between the second table and the constant vector, wherein the third predicate is a component of the query predicate.