Calculator Input
Enter attributes as comma-separated values. Write each dependency on a new line using the format A,B->C,D.
Example Data Table
| Relation | Functional Dependencies | Test Set | Closure | Super Key? |
|---|---|---|---|---|
| R(A, B, C, D, E) | A→B, B→C, CD→E | A, D | A, B, C, D, E | Yes |
| R(A, B, C, D) | A→B, B→C | A | A, B, C | No |
| R(P, Q, R, S) | P→Q, QR→S | P, R | P, Q, R, S | Yes |
Formula Used
Attribute Closure: Start with X+ = X. Repeatedly add every attribute on the right side of a dependency whose left side is already inside the closure.
Closure Update Rule: If Y ⊆ X+ and Y → Z, then update to X+ = X+ ∪ Z.
Super Key Test: A set X is a super key when X+ = R, where R is the full relation schema.
Candidate Key Test: A set is a candidate key when it is a super key and removing any one attribute makes it fail the super key test.
How to Use This Calculator
- Enter the full relation schema attributes in the first field.
- Type one functional dependency per line using the format A,B->C,D.
- Enter the attribute set you want to test as a possible super key.
- Submit the form to see the closure, super key verdict, and minimality result.
- Review the closure steps to understand exactly which dependency added each attribute.
- Check the candidate keys table to compare your tested set with minimal valid keys.
- Use the graph and downloadable reports for documentation or teaching notes.
FAQs
1. What does a super key mean?
A super key is any attribute set whose closure includes every attribute in the relation. It can uniquely identify tuples, but it may contain unnecessary extra attributes.
2. How is a candidate key different?
A candidate key is a minimal super key. It still determines the whole relation, but no attribute inside it can be removed without losing that property.
3. Why is closure important here?
Closure shows everything a tested attribute set can determine under the given dependencies. Comparing that closure with the full schema tells you whether the set is a super key.
4. Can one relation have many candidate keys?
Yes. Different minimal attribute combinations can determine the full relation. This calculator lists each candidate key it finds within the selected search limit.
5. Why does the calculator use a combination limit?
Searching all possible attribute subsets becomes expensive for large schemas. The limit keeps the page responsive while still allowing advanced analysis for typical classroom and design examples.
6. What input format should I use for dependencies?
Use comma-separated attributes on each side of an arrow, such as A,B->C,D. Put each dependency on a new line for best readability.
7. What happens if I reference attributes not in the schema?
The calculator adds them automatically and shows a note. That keeps the analysis consistent, though it is still better to define the full relation schema clearly yourself.
8. Is this useful for normalization work?
Yes. Super keys, candidate keys, and prime attributes are core pieces in normalization, decomposition checks, and dependency reasoning for structured relational database design.