19. The method of claim 18 , wherein determining the set of candidate queries and costs further comprises: determining a partial cost for a first portion of the certain query; and if the partial cost satisfies the first particular mathematical relationship with the current-best cost, determining a second cost based on the entire particular semantically equivalent query.
19. The method of claim 18 , wherein determining the set of candidate queries and costs further comprises: determining a partial cost for a first portion of the certain query; and if the partial cost satisfies the first particular mathematical relationship with the current-best cost, determining a second cost based on the entire particular semantically equivalent query. 20. The method of claim 19 , wherein choosing the particular query comprises, if the partial cost does not satisfy the first particular mathematical relationship with the current-best cost or if the second cost satisfies a second particular mathematical relationship with the current-best cost, then choosing as the particular query a candidate query other than the certain query.