Notion of Equivalent Relational Databases (RDBs)?

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Hi all,
RDB:=Relational Database
I need for this to determine if there is a standard, " reasonable" notion for when two RDBs are considered to be equivalent ( other than the obvious relabeling and reordering of fields). OF course, we assume that the Functional Dependency graphs are unique/fixed, up to graph isomorphism. I did a search, but it seems like anything useful is behind a pay wall.
 
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This is a hard question to answer.

On the lowest level, comparing database saves using CRC or something similar would be one way. It would basically say if two snapshots of a database were identical.

At a higher level, using the whole database schema comparing schema to schema, table to table, indexes to indexes at the user level would be another. It assumes the names of schema, tables, columns... are the same. This might show two databases implemented on different vendor platform are the same.

At the highest level, comparing schema design to design and how things are modeled to see if any data is left out by one of the databases where names of things are different but still represent the same things.

Usually what happens is a company say a bank wants to migrate to a new database system. They would insure that existing data is properly mapped into the new schema and that nothing needed is lost in the migration.

Companies like IBM, would offer comprehensive industry specific schemas for banking that banks would use if a bank merger was planned so they would now have a common database for the new organization. The vendor would also supply the necessary ETL tools to migrate the data and its relationships over to th new system.
 
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Thanks, Jedi, how about using Relational Algebra? And, what is CRC?