Calculator Inputs
Example Data Table
| Universal Attributes | Functional Dependencies | Decomposition | Expected Reading |
|---|---|---|---|
| A, B, C | A → B; B → C | R1(A, B); R2(B, C) | Preserves A → B and B → C. |
| A, B, C | A → B; B → C | R1(A, B); R2(A, C) | May miss B → C locally. |
| A, B, C, D | A → B; C → D | R1(A, B); R2(C, D) | Rules remain local in separate relations. |
Formula Used
Attribute closure: Start with X. Repeatedly add Y whenever a dependency Z → Y exists and Z is contained in the current closure.
Dependency preservation: A decomposition is dependency preserving when every dependency in F can be inferred from the union of all projected dependencies.
Projection: For each relation Ri, project rules that use only attributes inside Ri and are implied by the original dependency set.
Lossless check: The chase method applies dependencies to a symbolic table. A full universal row indicates a lossless join.
How to Use This Calculator
- Enter every attribute from the original universal relation.
- Enter one functional dependency per line using the arrow format.
- Enter each decomposed relation on a separate line.
- Add an optional attribute set when you want a closure result.
- Click the calculate button and read the result above the form.
- Use CSV or PDF buttons to export the displayed summary.
Dependency Preserving Decomposition Guide
What This Calculator Does
A dependency preserving decomposition calculator helps database designers test a relational split before implementation. It compares the original functional dependencies with dependencies that can be checked inside each decomposed relation. The goal is simple. Every important rule should remain enforceable without joining tables repeatedly.
Why Dependency Preservation Matters
When a design is not dependency preserving, validation becomes harder. The database may need joins just to confirm a constraint. That adds cost, slows inserts, and increases application logic. A preserved design keeps constraints local. Each table can protect its own rules more easily.
How The Check Works
The calculator first reads the universal attributes. It then parses each functional dependency. Next, it reads every decomposed relation. For each relation, it projects dependencies from the original set. A projected dependency uses attributes inside that relation only. The tool unites those projections and tests whether every original dependency can still be derived.
Closures And Keys
Attribute closure is central to the result. The closure of X contains every attribute determined by X under available rules. If X closure contains all attributes, X is a superkey. A candidate key is a minimal superkey. This calculator lists candidate keys when the attribute count is practical.
Lossless Join Insight
Dependency preservation is not the only design concern. A decomposition should also avoid spurious tuples. The calculator includes a chase based lossless join check. It builds a symbolic table, applies dependencies, and checks whether a full universal row appears. This gives useful guidance for normal form decisions.
Using The Results
Start with clear attribute names. Use commas for multi character names. Enter dependencies with one arrow, such as A,B -> C. Place each decomposed relation on its own line. After calculation, review preserved and missing dependencies first. Then inspect projected dependencies, keys, and lossless status.
Good Design Practice
A strong relational design balances normalization, dependency preservation, and lossless joins. Sometimes a fully normalized design sacrifices local constraint checking. Sometimes a practical design adds a relation to preserve dependencies. Use the result as a design assistant, not as a replacement for expert review. Export reports after each run. Share them with classmates, auditors, developers, or clients when design choices need clear supporting evidence later.
FAQs
What is dependency preservation?
Dependency preservation means the original functional dependencies can be checked using dependencies inside the decomposed relations, without joining all tables first.
What input format should I use?
Use comma separated attributes. Write dependencies like A,B -> C. Put each decomposed relation on a new line, such as R1(A,B).
Does preservation mean the design is always good?
No. A design should also be checked for lossless join, redundancy, update anomalies, and normal form goals.
What is a projected dependency?
A projected dependency is a rule implied by the original dependencies that uses only attributes from one decomposed relation.
What is attribute closure?
Attribute closure is the set of all attributes that can be determined from a starting attribute set using functional dependencies.
Why are candidate keys useful?
Candidate keys show minimal attribute sets that identify full tuples. They help judge normalization and relation structure.
Can I use multi character attributes?
Yes. Use commas between names, such as StudentID, CourseID, Grade. This prevents the parser from reading each character separately.
What does a missing dependency mean?
It means the dependency was not derived from projected dependencies. The design may need another relation or a revised decomposition.