Formula Used
Attribute closure: X+ is found by repeatedly adding attributes Y when a dependency X → Y has its left side inside the current closure.
Projection: For each decomposed relation Ri, the calculator checks subsets X of Ri. It adds X → A when A is in X+ and A also belongs to Ri.
Preservation test: A decomposition is dependency preserving when every dependency in a minimal cover of F can be derived from the union of all projected dependencies.
Score: Preservation score = preserved dependencies ÷ tested dependencies × 100.
How To Use This Calculator
Enter the universal relation attributes first. Add functional dependencies line by line. Then enter each decomposed relation. Press the calculate button. Read the score, missing dependency list, closure comparison, projected covers, candidate keys, and chase note. Export the result when you need a report.
Dependency Preservation in Database Design
Dependency preservation is a practical check during normalization. It asks one direct question. Can the original functional dependencies be enforced after a relation is decomposed? A good design should reduce redundancy. It should also keep rules easy to test. When preservation fails, the database may need expensive joins before constraints can be verified.
Why This Calculator Helps
This calculator compares the original dependencies with dependencies projected onto each decomposed relation. It computes attribute closures. It creates a minimal cover. It then checks whether every essential rule can still be derived from the projected rules. The result gives a clear preserved or missing status for each dependency.
How To Read The Score
A high score means most design rules survived the decomposition. A perfect score means the tested cover is preserved. A low score means some rules may require joining decomposed tables. That can make validation slower. It may also increase application logic. Use the missing dependency list to decide whether another decomposition is better.
Useful Design Notes
Dependency preservation is not the same as lossless join. A design can be lossless but still not preserve dependencies. A design can also preserve dependencies while still needing review for normal form quality. For strong schema work, check preservation, lossless join, candidate keys, and redundancy together. This tool includes those supporting views so decisions are easier.
Best Practice
Start with a clean universal relation. Enter each functional dependency on its own line. Keep attribute names consistent. Then enter decomposed relations. Review the minimal cover before trusting the final result. If a needed dependency is missing, adjust the relation split. You may add a relation that contains the attributes required to enforce that rule locally.
Limits To Remember
Projection can grow quickly when many attributes exist in one relation. This page uses a subset cap to keep calculations responsive. Raise the cap for deeper checks. Lower it for quick screening. Treat any truncation warning carefully. It means the displayed preservation result may be conservative. Always confirm critical academic, audit, or production designs with formal review. Small examples are best for learning. Larger schemas need careful naming and validation too.
FAQs
What is dependency preservation?
Dependency preservation means original functional dependencies can be enforced using only dependencies inside decomposed relations. It avoids joining tables just to validate design rules.
Is dependency preservation the same as lossless join?
No. Lossless join checks whether decomposed relations can rebuild the original relation. Dependency preservation checks whether rules remain enforceable after decomposition.
Why does the calculator use a minimal cover?
A minimal cover removes redundant dependency parts. Testing it gives a compact and equivalent rule set, making preservation results easier to read.
Can I use multi-character attribute names?
Yes. Use commas between names, such as StudentID, CourseID, Grade. This prevents the parser from treating letters as separate attributes.
What does a missing dependency mean?
It means the projected dependencies do not derive that rule. The database may need joins or extra checks to enforce it reliably.
Why is there a subset cap?
Projection can require many subset checks. The cap protects page speed. Increase it when relations have many attributes and you need deeper analysis.
Does a perfect score prove the schema is ideal?
No. It proves the tested dependencies are preserved. You should still review normal forms, keys, redundancy, and lossless join behavior.
Can this tool replace formal database review?
No. It is a helpful design checker. For exams, audits, or production systems, confirm results with formal methods and expert review.