# Reduction Builder

> Construct and verify polynomial-time reductions between computational problems

- Skill: `a5c-ai/reduction-builder` (Agent Skill)
- Install (CLI): `npx skillmds@latest add a5c-ai/reduction-builder`
- Raw SKILL.md: https://api.skillmd.com/api/skills/a5c-ai/reduction-builder/raw
- Safety review: pending (external: skill-scanner PASS, skillspector PASS)
- Works with: Claude Code, Claude.ai, OpenAI Codex
- Category: Coding & Dev Tools
- Author: a5c-ai (https://skillmd.com/u/a5c-ai)
- Updated: 2026-09-09
- Page: https://skillmd.com/skills/a5c-ai/reduction-builder

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# Reduction Builder

## Purpose

Provides expert guidance on constructing polynomial-time reductions for NP-completeness proofs and problem classification.

## Capabilities

- Gadget library for common reductions (3-SAT, Vertex Cover, etc.)
- Reduction verification (correctness in both directions)
- Polynomial-time verification
- Visualization of gadget constructions
- Generate reduction documentation
- Chain multiple reductions

## Usage Guidelines

1. **Problem Analysis**: Understand source and target problem structures
2. **Gadget Selection**: Choose or design appropriate gadgets
3. **Reduction Construction**: Build the polynomial-time mapping
4. **Correctness Proof**: Prove both directions of the reduction
5. **Time Analysis**: Verify polynomial running time

## Tools/Libraries

- Graph visualization
- LaTeX documentation
- Formal verification tools