Dependency Preservation Calculator

Check projected dependencies with closures and decomposition reports. Find preserved rules and hidden gaps quickly. Export results for review, teaching, and schema design tasks.

Calculator Input

Use commas for long names. Compact ABC is read as A,B,C.
This only limits displayed projection lists.
Turn this off for very large schemas.

The report checks whether original dependencies follow from the union of projected dependencies.

Example Data Table

Item Example Value Purpose
Relation R(A,B,C,D,E) Main attribute set
Dependencies A -> B; B -> C; C,D -> E; A,D -> E Rules to preserve
Decomposition R1(A,B,C), R2(A,D), R3(C,D,E) Proposed smaller schemas
Expected result Dependency preserving Every sample rule can be inferred

Formula Used

Let F be the original set of functional dependencies. Let the decomposition be D = {R1, R2, ..., Rn}. The projection of F on Ri is πRi(F), which contains dependencies X -> Y where X and Y are inside Ri and F logically implies X -> Y.

The decomposition is dependency preserving when F+ equals or is covered by (πR1(F) ∪ πR2(F) ∪ ... ∪ πRn(F))+. In practice, each original rule X -> Y is checked by computing X+ under the projected rules. If Y is inside that closure, the rule is preserved.

How to Use This Calculator

  1. Enter all attributes of the original relation.
  2. Enter one functional dependency per line, such as A,B -> C.
  3. Enter each decomposed schema on a new line.
  4. Choose whether to show projected dependency details.
  5. Press Calculate to see the result below the header.
  6. Use CSV or PDF to save the report.

Dependency Preservation in Practice

Dependency preservation matters when a relation is split into smaller relations. A design may remove update anomalies. Yet it should still allow important rules to be checked without joining every table. This calculator studies that issue with functional dependencies and decomposition schemas.

What the Tool Checks

The tool compares the original dependency set with the dependencies that can be enforced inside each decomposed relation. It first parses attributes, left sides, right sides, and relation fragments. It then computes closures. A closure shows every attribute that follows from a chosen attribute set. If every original rule can be derived from projected rules, the decomposition is dependency preserving.

Why This Is Useful

Normalization often creates cleaner tables. It can also move related attributes apart. When a rule crosses several fragments, a database may need joins to validate it. That can slow validation and complicate constraints. A dependency preservation check warns you before that design reaches production.

Advanced Review Details

The report includes a canonical cover, projected dependency summaries, and per rule closure results. The canonical cover removes repeated or redundant rules. Projection summaries show which rules belong to each decomposed schema. The per rule test explains whether each dependency is preserved or missing. This makes the result easier to audit.

How to Read Results

A preserved result means the right side of a dependency appears in the closure of its left side under the projected rules. A missing result means at least one right side attribute could not be inferred. Review those missing rules carefully. You may need another fragment, a different decomposition, or an added constraint.

Design Advice

Use small attribute names for quick experiments, such as A, B, C, and D. Use comma separated names for real schemas. Test both the proposed design and close alternatives. A dependency preserving design is not always lossless, and a lossless design is not always dependency preserving. Treat this report as one normalization checkpoint, not the whole design decision.

Keep examples realistic. Include every rule used by application logic, reports, and data entry screens. A rule that looks minor can become costly after decomposition. Save the CSV or document report when you compare versions. It helps reviewers follow schema change.

FAQs

What is dependency preservation?

Dependency preservation means original functional dependencies can still be enforced after decomposition without rebuilding the full original relation through joins.

What input format should I use?

Enter one dependency per line. Use A -> B for compact attributes or Student,Course -> Instructor for named attributes.

Does this calculator test lossless join?

No. It focuses on dependency preservation. Lossless join is a separate normalization property and should be checked with its own test.

Why does a dependency show as missing?

It shows as missing when the right side cannot be inferred from the left side using dependencies available inside decomposed schemas.

What is a projected dependency?

A projected dependency is a rule that only uses attributes from one decomposed relation and follows from the original dependency set.

What is the canonical cover?

A canonical cover is a simplified dependency set. It removes repeated rules, redundant rules, and unnecessary attributes where possible.

Can I use long attribute names?

Yes. Use comma separated names, such as StudentID,CourseID -> InstructorID. Avoid compact typing when names contain several letters.

Can I export the result?

Yes. Use the CSV button for spreadsheet review. Use the PDF button for a portable report.

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