Check decompositions, closures, and dependency rules with confidence. Improve structured database planning for crawlable, organized, and scalable technical content systems online.
| A | B | C | D |
|---|---|---|---|
| 1 | x | m | n |
| 2 | x | m | n |
| 3 | y | p | q |
A binary decomposition of relation R into R1 and R2 is lossless when the common attributes functionally determine one side.
Test: (R1 ∩ R2) → (R1 − R2) or (R1 ∩ R2) → (R2 − R1)
The calculator computes the closure of the intersection using the given functional dependencies. If that closure contains all attributes from either difference set, the join is lossless.
Closure Rule: X+ starts with X. Repeatedly add attributes implied by any dependency whose left side is already inside X+.
Enter the original relation attributes first. Then add the two decomposed relations. List each functional dependency on a new line.
Submit the form to see the intersection, attribute closure, side differences, and final result. The result appears above the form for quick review.
You can also enter a small example table. This helps teams explain decomposition choices during audits, schema cleanup, technical SEO reviews, or structured content design.
Use the CSV button to export the result summary. Use the PDF button to create a print-ready report.
Lossless join analysis helps preserve data accuracy after decomposition. It ensures split tables can rebuild the original relation without adding false combinations. This matters in structured content systems, data warehouses, and schema planning.
Many websites store product, author, page, and metadata records across linked tables. A lossless split keeps relationships clean. That supports dependable reporting, consistent indexing signals, and better structured data management across platforms.
This calculator uses the classic binary lossless join rule. It finds the intersection of the two decomposed relations. Then it computes the closure of that intersection using the listed functional dependencies. If the closure determines one full side difference, the split is safe.
Closure reveals everything implied by a chosen attribute set. It is the core step behind normalization checks. Instead of guessing, teams can prove whether common attributes retain enough information to reconstruct the original row set correctly.
Advanced users often review table decomposition before migrations or performance changes. This tool gives a readable result, useful explanation, and export options. It supports audits, documentation, teaching, and validation during schema updates or technical cleanup projects.
A lossless join means decomposed relations can be joined back without creating extra tuples. The original information remains intact after decomposition.
The calculator uses the binary decomposition rule. It checks whether the common attributes determine all attributes on one side of the decomposition.
Functional dependencies describe attribute rules inside a relation. They let the calculator compute closures and verify whether the decomposition preserves reconstructability.
This version focuses on two-way decomposition. That keeps the logic clear and practical for most teaching, review, and planning scenarios.
Attribute closure is the full set of attributes implied by a starting set under the listed dependencies. It is central to normalization analysis.
The example table helps users explain the schema visually. It supports walkthroughs, documentation, and validation discussions with teams or clients.
Yes. Clean relational design can improve metadata storage, content mapping, and structured record consistency in larger publishing or ecommerce systems.
The CSV export saves the main decision fields. The PDF option creates a printable summary of the calculated result and explanation.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.