docs: Add reduction classification and detailed survey

[GiggleLiu]

Summary

• Add Typst mathematical document (docs/paper/reductions.typ) with formal problem definitions, reduction theorems, and proofs
• Classify all reductions as trivial (6) vs non-trivial (7)
• Provide detailed survey of non-trivial reductions with academic references
• Add JSON export capability for reduction graph with automatic layered layout
• Update mdBook documentation with Mermaid diagrams and expanded content

Classification

Trivial Reductions

Reduction	Transformation
IS ↔ VC	Complement: S is IS iff V\S is VC
IS → SetPacking	Vertex → set of incident edges
Matching → SetPacking	Edge (u,v) → set {u, v}
VC → SetCovering	Vertex → set of incident edge indices
k-SAT → SAT	Direct embedding
QUBO ↔ SpinGlass	Variable substitution s = 2x - 1

Non-Trivial Reductions

Reduction	Key Technique
SAT → k-SAT	Clause splitting with auxiliary variables
SAT → IS	Karp's conflict graph (clique + complement edges)
SAT → Coloring	5-vertex OR-gadgets
SAT → DominatingSet	Variable triangles
CircuitSAT → SpinGlass	Logic gate Hamiltonians
Factoring → CircuitSAT	Array multiplier with full adders
SpinGlass ↔ MaxCut	Ancilla vertex for external fields

Files Changed

• docs/paper/reductions.typ - Typst document with math definitions
• docs/paper/references.bib - Academic bibliography
• docs/paper/reduction_graph.json - Auto-generated graph data
• src/rules/graph.rs - JSON export and layout algorithm
• examples/export_graph.rs - Example to generate JSON
• docs/src/reductions/*.md - Updated mdBook pages

Test plan

• All 639 tests pass
• Typst document compiles successfully
• JSON export works via cargo run --example export_graph

🤖 Generated with Claude Code

[codecov]

Codecov Report

❌ Patch coverage is 98.20359% with 6 lines in your changes missing coverage. Please review.
✅ Project coverage is 97.97%. Comparing base (c64ac3f) to head (cee4c8f).
⚠️ Report is 1 commits behind head on main.

Files with missing lines	Patch %	Lines
src/rules/graph.rs	98.20%	6 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main       #9      +/-   ##
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+ Coverage   97.94%   97.97%   +0.03%     
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  Files          55       55              
  Lines       11373    11659     +286     
==========================================
+ Hits        11139    11423     +284     
- Misses        234      236       +2     

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[Copilot]

Pull request overview

This PR adds comprehensive documentation for problem reductions, including a formal Typst mathematical document with proofs, academic citations, and automated visualization capabilities. The changes classify reductions as trivial (6) vs non-trivial (7) and provide detailed academic references.

Changes:

• Added JSON export functionality to ReductionGraph with automatic layered layout computation using a simplified Sugiyama algorithm
• Created Typst mathematical document (docs/paper/reductions.typ) with formal problem definitions, reduction theorems, and constructive proofs
• Expanded mdBook documentation with Mermaid diagrams, academic citations, and detailed reduction explanations
• Added build automation for generating the reduction graph JSON and compiling the Typst paper

Reviewed changes

Copilot reviewed 13 out of 14 changed files in this pull request and generated 5 comments.

Show a summary per file

File	Description
src/rules/mod.rs	Exports new JSON-related types (NodeJson, EdgeJson, ReductionGraphJson)
src/rules/graph.rs	Implements JSON export, bidirectional edge detection, and layered graph layout algorithm
examples/export_graph.rs	Example program to export reduction graph to JSON file
docs/src/reductions/index.md	Updated with additional reduction mappings
docs/src/reductions/graph.md	Added Mermaid flowchart diagram and expanded API documentation
docs/src/reductions/available.md	Comprehensive documentation with academic citations for all reductions
docs/src/problems/satisfiability.md	Expanded with formal definitions, complexity notes, and reduction examples
docs/paper/references.bib	BibTeX bibliography with 8 academic references
docs/paper/reductions.typ	Typst document with formal mathematical definitions and proofs
docs/paper/reduction_graph.json	Auto-generated JSON representation of reduction graph
book.toml	Added Mermaid preprocessor and JavaScript configuration
Makefile	Added targets for mdbook, paper compilation, and documentation building
mermaid-init.js	JavaScript for Mermaid theme handling in mdBook

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[Copilot]

The nguyen2023 reference is defined in the bibliography but is never cited in the Typst document (reductions.typ). This is an unused reference that should either be removed or cited in the document if it's relevant to the content.

Suggested change

	@article{nguyen2023,
	author = {Manh-Tien Nguyen and Jin-Guo Liu and others},
	title = {Tensor network message passing},
	journal = {PRX Quantum},
	volume = {4},
	pages = {010316},
	year = {2023}
	}

[Copilot]

The Gavril 1972 reference is cited in the mdBook documentation (docs/src/reductions/available.md) but is missing from the BibTeX file (references.bib). To maintain consistency and academic rigor, this reference should be added to the bibliography.

The citation should be:
@Article{gavril1972,
author = {Fănică Gavril},
title = {Algorithms for Minimum Coloring, Maximum Clique, Minimum Covering by Cliques, and Maximum Independent Set of a Chordal Graph},
journal = {SIAM Journal on Computing},
volume = {1},
number = {2},
pages = {180--187},
year = {1972}
}

[Copilot]

The layout computation at line 429 calculates total_width as (nodes.len() as f64 - 1.0) * x_spacing, which will result in a negative value when nodes.len() is 0 (an empty layer). While this edge case is unlikely in practice since layers are created from non-empty groups, it would be more robust to handle this case explicitly or add a comment indicating that empty layers cannot occur. The calculation would be more defensive as: let total_width = nodes.len().saturating_sub(1) as f64 * x_spacing;

[Copilot]

The book.toml configuration references "mermaid.min.js" in the additional-js array (line 16), but this file does not appear to exist in the repository. The mdbook-mermaid preprocessor typically provides the necessary Mermaid JavaScript automatically, so including mermaid.min.js here is likely redundant and may cause errors if the file is missing. Consider removing "mermaid.min.js" from the additional-js array and relying on the preprocessor to inject the necessary scripts, or ensure the file is properly included if it's needed for a specific reason.

Suggested change

	additional-js = ["mermaid.min.js", "mermaid-init.js"]
	additional-js = ["mermaid-init.js"]

[Copilot]

The citation for the Factoring to CircuitSAT reduction attributes the multiplier circuit construction to Shor 1994. However, Shor's paper focuses on quantum algorithms for factoring, not the classical reduction from factoring to CircuitSAT via multiplier circuits. This reduction is actually folklore in computational complexity theory and predates Shor's work. The Typst document correctly labels this as "Folklore" in the summary table. This citation should either be removed or replaced with a more appropriate reference, or the comment should clarify that Shor's work is related but not the original source of this particular reduction.