Fix #414: [Model] LongestCommonSubsequence

[GiggleLiu]

Summary

• add an execution plan for issue [Model] LongestCommonSubsequence #414
• refactor the existing LongestCommonSubsequence stack to match the issue's decision-model contract
• keep the ILP, CLI, tests, examples, and paper entries aligned during execution

Fixes #414

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 97.17%. Comparing base (057025f) to head (842c792).
⚠️ Report is 1 commits behind head on main.

Additional details and impacted files

@@           Coverage Diff           @@
##             main     #666   +/-   ##
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  Coverage   97.17%   97.17%           
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  Files         304      304           
  Lines       40108    40061   -47     
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- Hits        38976    38931   -45     
+ Misses       1132     1130    -2     

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[GiggleLiu]

Implementation Summary

Changes

• Reworked LongestCommonSubsequence into the issue-414 decision model with alphabet_size, strings, and bound, plus satisfaction semantics, canonical examples, and updated paper/example-db wiring.
• Replaced the existing LongestCommonSubsequence -> ILP reduction with a bounded-witness feasibility encoding that uses symbol-selection variables, per-string match-position variables, ordering constraints, and witness extraction.
• Updated CLI creation support for LCS to require --strings and --bound, support both numeric strings (0,1,0;1,0,1) and compact raw-string input (010110;100101), and refresh the help text/examples.
• Rewrote the LCS model/rule/unit tests and refreshed generated docs artifacts (examples.json, problem_schemas.json, reduction_graph.json) and the paper section/reference entry.

Deviations from Plan

• The repository already contained an older optimization-oriented LongestCommonSubsequence model and ILP rule on main, so the work was a semantic refactor of those existing files rather than a net-new model/rule addition.
• The implementation accepts the degenerate bound = 0 case for library consistency, even though the issue statement focuses on positive K.

Open Questions

• None.

[Copilot]

Pull request overview

This PR implements the Issue #414 decision-model contract for LongestCommonSubsequence (fixed witness length K), refactors the ILP reduction to a feasibility formulation that supports multiple strings, and updates CLI/docs/examples/tests to match the new schema and semantics.

Changes:

• Refactor LongestCommonSubsequence from an optimization/selection model to a SatisfactionProblem with (alphabet_size, strings, bound) and witness-as-config semantics.
• Replace the LCS→ILP reduction with a bounded-witness feasibility ILP (symbol-choice + per-string embedding variables + monotonicity constraints).
• Align unit tests, CLI pred create parsing/help, example fixtures, and generated docs/paper content with the new model.

Reviewed changes

Copilot reviewed 13 out of 13 changed files in this pull request and generated 3 comments.

Show a summary per file

File	Description
src/unit_tests/trait_consistency.rs	Adds trait-consistency coverage for the updated LCS model.
src/unit_tests/rules/longestcommonsubsequence_ilp.rs	Updates ILP reduction tests to the new bounded-witness feasibility formulation.
src/unit_tests/models/misc/longest_common_subsequence.rs	Rewrites model tests for new schema, boolean metric, and witness configs.
src/rules/longestcommonsubsequence_ilp.rs	Refactors the rule to build a feasibility ILP for bounded-witness LCS over multiple strings.
src/models/misc/mod.rs	Registers canonical example specs for the LCS model.
src/models/misc/longest_common_subsequence.rs	Implements the new decision/satisfaction LCS model and variant complexity.
src/example_db/fixtures/examples.json	Adds/updates canonical examples for the new LCS model and its ILP reduction.
problemreductions-cli/src/commands/create.rs	Updates pred create help + parsing for LCS (strings, bound, alphabet-size).
problemreductions-cli/src/cli.rs	Updates CLI flag listing/docs for LCS arguments.
docs/src/reductions/reduction_graph.json	Regenerates reduction graph data for updated complexity/overhead formulas.
docs/src/reductions/problem_schemas.json	Regenerates schema docs to reflect new LCS fields/types.
docs/paper/references.bib	Adds Wagner–Fischer reference for the LCS discussion.
docs/paper/reductions.typ	Updates paper section and ILP reduction description to the bounded-witness decision model.

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