Fix #445: [Model] AdditionalKey

[GiggleLiu]

Summary

Add the AdditionalKey satisfaction problem model from relational database theory (Garey & Johnson A4 SR27). This NP-complete problem asks whether a relational schema has a candidate key not in a given set of known keys.

Fixes #445

[codecov]

Codecov Report

❌ Patch coverage is 96.08696% with 9 lines in your changes missing coverage. Please review.
✅ Project coverage is 97.03%. Comparing base (dfcc313) to head (262f635).

Files with missing lines	Patch %	Lines
src/models/misc/additional_key.rs	93.23%	9 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #681      +/-   ##
==========================================
- Coverage   97.04%   97.03%   -0.01%     
==========================================
  Files         284      286       +2     
  Lines       38037    38267     +230     
==========================================
+ Hits        36914    37134     +220     
- Misses       1123     1133      +10     

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[GiggleLiu]

Implementation Summary

Changes

• src/models/misc/additional_key.rs — New model: AdditionalKey satisfaction problem (struct, constructor, closure computation, Problem/SatisfactionProblem trait impls, declare_variants!, canonical example-db entry)
• src/unit_tests/models/misc/additional_key.rs — 13 unit tests (creation, evaluation, brute force, serialization, paper example)
• src/models/misc/mod.rs — Module registration + example-db chain
• src/models/mod.rs — Re-export
• src/lib.rs — Prelude re-export
• problemreductions-cli/src/cli.rs — CLI flags (--num-attributes, --dependencies, --relation-attrs, --known-keys)
• problemreductions-cli/src/commands/create.rs — pred create AdditionalKey handler
• src/example_db/fixtures/examples.json — Regenerated with new model
• docs/paper/reductions.typ — problem-def("AdditionalKey") with display name, formal definition, background, and worked example
• docs/paper/references.bib — Added beeri1979 citation

Deviations from Plan

• src/unit_tests/trait_consistency.rs was removed in a prior refactor — skipped that step
• Added AdditionalKey to prelude in src/lib.rs (discovered during spec review)

Open Questions

• None

Verification

• make test: 2173 tests passed
• make clippy: clean
• make paper: compiles cleanly

[Copilot]

Pull request overview

Adds a new NP-complete satisfaction model, AdditionalKey, representing the “additional candidate key” problem from relational database theory, and wires it into the library exports, CLI instance creation, examples, and paper.

Changes:

• Introduce AdditionalKey model (schema registration, evaluation via FD closure + minimality + exclusion from known keys, example-db spec).
• Add unit tests covering evaluation behavior, brute force solving, and serde round-trip.
• Extend CLI pred create with new flags/parsing for AdditionalKey, and add an example-db fixture plus paper reference/definition.

Reviewed changes

Copilot reviewed 10 out of 10 changed files in this pull request and generated 3 comments.

Show a summary per file

File	Description
src/models/misc/additional_key.rs	New AdditionalKey model implementation, schema registration, variants declaration, and example-db spec.
src/unit_tests/models/misc/additional_key.rs	Unit tests for correctness, solver integration, and serialization.
src/models/misc/mod.rs	Registers the new misc module, re-exports AdditionalKey, and includes its example specs.
src/models/mod.rs	Re-exports AdditionalKey from models::misc.
src/lib.rs	Adds AdditionalKey to the crate prelude exports.
problemreductions-cli/src/cli.rs	Adds AdditionalKey CLI flags to CreateArgs and the “Flags by problem type” help section.
problemreductions-cli/src/commands/create.rs	Adds AdditionalKey instance parsing/creation and an example invocation string.
src/example_db/fixtures/examples.json	Adds an AdditionalKey model fixture with sample/optimal satisfying configs.
docs/paper/references.bib	Adds Beeri & Bernstein (1979) reference.
docs/paper/reductions.typ	Adds paper definition block and display name mapping for AdditionalKey.

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