reduction-builder

name	reduction-builder
description	Construct and verify polynomial-time reductions between computational problems
allowed-tools	["Bash","Read","Write","Edit","Glob","Grep"]
metadata	{"specialization":"computer-science","domain":"science","category":"complexity-theory","phase":6}
graph	{"domains":["domain:computer-science"],"specializations":["specialization:theoretical-computer-science"],"skillAreas":["skill-area:np-hard-heuristics","skill-area:graph-algorithms","skill-area:mathematical-reasoning"],"workflows":["workflow:research-grant-lifecycle"],"roles":["role:computational-scientist","role:research-engineer"]}

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