Complexity Class Oracle

---
name: complexity-class-oracle
description: Classify problems into complexity classes with supporting evidence and proof strategies
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]
---

# Complexity Class Oracle

## Purpose

Provides expert guidance on classifying computational problems into complexity classes and understanding class relationships.

## Capabilities

- Determine membership in P, NP, co-NP, PSPACE, EXPTIME
- Identify complete problems for each class
- Query known complexity results database
- Suggest proof strategies for classification
- Generate complexity landscape diagrams
- Explain class inclusions and separations

## Usage Guidelines

1. **Problem Characterization**: Formalize the computational problem
2. **Class Investigation**: Check membership in relevant classes
3. **Evidence Collection**: Gather evidence for classification
4. **Strategy Selection**: Choose proof strategy for membership
5. **Documentation**: Generate classification report

## Tools/Libraries

- Complexity Zoo database
- Diagram generation
- LaTeX documentation