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

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