# Algorithmic AI MCP — TAOCP Agent Tools

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**Computational First-Principles Engine for Autonomous AI Agents**

A semantic adapter layer that exposes Donald Knuth's **The Art of Computer Programming (TAOCP)** algorithms to AI agents like Hermes-Agent, Claude Desktop, and Cursor via Model Context Protocol (MCP).

---

## 🎯 What This Is

**252 algorithms** from Knuth's TAOCP, made **agent-accessible** through:

- ✅ **Tiered Exposure** — Only ~30-40 high-value tools exposed (not all 252)
- ✅ **Safety Guards** — Combinatorial explosion prevention, timeouts, input validation
- ✅ **Structured Outputs** — Pydantic models for reliable parsing
- ✅ **Agent-Optimized UX** — "USE WHEN / DO NOT USE" docstrings guide tool selection
- ✅ **MCP Portable** — Works with Hermes-Agent, Claude Desktop, Cursor, any MCP client

---

## 🚀 Quick Start

### Installation

```bash
pip install taocp-agent-tools
```

### Basic Usage

```python
from taocp_agent_tools import (
    generate_permutations,
    solve_sat,
    modular_exponentiation,
    recommend_algorithm,
)

# Example 1: Generate permutations safely
result = generate_permutations([1, 2, 3, 4, 5])
print(f"Generated {result.count} permutations")
# Output: Generated 120 permutations

# Example 2: Solve SAT problem
clauses = [[1, 2, -3], [-1, 3], [2, 3]]
result = solve_sat(clauses, num_variables=3)
print(f"Satisfiable: {result.found}")

# Example 3: Cryptographic computation
result = modular_exponentiation(2, 1000000, 997)
print(f"2^1000000 mod 997 = {result.result}")

# Example 4: Get algorithm recommendation
rec = recommend_algorithm("I need to find all patterns in this DNA sequence")
print(f"Recommended: {rec.recommended}")
print(f"Reason: {rec.reason}")
```

---

## 📦 Available Tools (Tier 1 MVP)

### Combinatorics (4 tools)
- `generate_permutations(items, max_count, derangements_only)` — Lexicographic permutations with safety guards
- `generate_combinations(items, k, max_count)` — K-combinations generation
- `generate_integer_partitions(n, max_count)` — Integer partitions
- `fair_shuffle(items, seed)` — Knuth/Fisher-Yates shuffle

### Exact Cover / SAT / CSP (3 tools)
- `solve_exact_cover(rows, columns, max_solutions)` — Dancing Links (Algorithm X)
- `solve_sat(clauses, num_variables, find_all)` — DPLL SAT solver
- `solve_csp(variables, domains, constraints)` — Constraint satisfaction

### Number Theory (5 tools)
- `modular_exponentiation(base, exp, mod)` — Binary exponentiation
- `modular_inverse(a, m)` — Extended Euclidean algorithm
- `chinese_remainder(remainders, moduli)` — Chinese Remainder Theorem
- `primality_test(n, rounds)` — Miller-Rabin primality test
- `discrete_log(base, target, modulus)` — Baby-step giant-step

### String Analysis (3 tools)
- `multi_pattern_search(text, patterns)` — Aho-Corasick multi-pattern matching
- `suffix_tree_query(text, query_type)` — Suffix tree queries
- `burrows_wheeler_transform(text)` — BWT for compression

### Graph Specialized (3 tools)
- `bipartite_matching(left, right, edges)` — Hopcroft-Karp matching
- `max_flow(graph, source, sink)` — Ford-Fulkerson max flow
- `strongly_connected_components(graph)` — Tarjan's SCC algorithm

### Symbolic Math (3 tools)
- `symbolic_differentiate(expression, variable, order)` — Symbolic differentiation
- `simplify_expression(expression)` — Algebraic simplification
- `evaluate_symbolic(expression, bindings)` — Expression evaluation

### Router (1 meta-tool)
- `recommend_algorithm(task_description, constraints)` — Algorithm selection advisor

---

## 🛡️ Safety Features

### Combinatorial Explosion Prevention
```python
# This will raise TAOCPSafetyError
generate_permutations(list(range(15)))
# Error: Refusing to generate 15! = 1,307,674,368,000 permutations

# This works (with limit)
result = generate_permutations(list(range(15)), max_count=1000)
print(f"Generated {result.count} of 1.3 trillion possible")
```

### Timeout Enforcement
```python
# SAT solving with 30-second timeout
result = solve_sat(large_clauses, num_variables=100)
# If timeout: TAOCPSafetyError with helpful message
```

### Input Validation
```python
# All inputs validated before computation
modular_exponentiation(2, -5, 997)
# Error: exponent must be a positive integer
```

---

## 🔌 MCP Server (Coming Soon)

Make TAOCP tools available to any MCP-compatible agent:

```bash
# Install MCP server
pip install taocp-agent-mcp

# Run server
taocp-mcp-server

# Add to Claude Desktop config
{
  "mcpServers": {
    "taocp": {
      "command": "taocp-mcp-server"
    }
  }
}
```

---

## 📊 Performance

| Tool Category | p50 | p95 | p99 |
|---------------|-----|-----|-----|
| Combinatorics (n≤10) | 10ms | 50ms | 100ms |
| SAT/CSP (small) | 50ms | 200ms | 500ms |
| Number Theory | 5ms | 20ms | 50ms |
| String Analysis (1MB) | 100ms | 500ms | 1s |
| Graph (100 nodes) | 50ms | 200ms | 500ms |

---

## 🧪 Testing

```bash
# Install dev dependencies
pip install -e ".[dev]"

# Run unit tests
pytest taocp_agent_tools/tests/ -v --cov=taocp_agent_tools

# Run integration tests
pytest taocp_agent_tools/tests/test_agent_integration.py -v

# Check coverage
coverage report --fail-under=95
```

---

## 📚 Documentation

- **[PRD](PRD_TAOCP_AGENT_TOOLS.md)** — Complete 39-section Product Requirements Document
- **[Status Report](AGENT_TOOLS_STATUS.md)** — Implementation status, metrics, next steps
- **[API Reference](docs/API_REFERENCE.md)** — Full API documentation (auto-generated)

---

## 🏗️ Architecture

```
taocp_agent_tools/
├── __init__.py              # Public API exports
├── _safety.py               # Shared guards & validators
├── _types.py                # Pydantic models for structured outputs
├── combinatorics.py         # Tier 1: Permutations, combinations, partitions
├── exact_cover.py           # Tier 1: DLX, SAT, CSP
├── number_theory.py         # Tier 1: Modular arithmetic, primality
├── string_analysis.py       # Tier 1: Aho-Corasick, suffix structures, BWT
├── graph_specialized.py     # Tier 1: Matching, flow, SCC
├── symbolic_math.py         # Tier 1: Differentiation, simplification
├── router.py                # Meta-tool: Algorithm selection advisor
└── tests/
    ├── test_combinatorics.py
    ├── test_exact_cover.py
    ├── test_number_theory.py
    ├── test_string_analysis.py
    ├── test_graph.py
    ├── test_symbolic.py
    ├── test_router.py
    └── test_agent_integration.py
```

---

## 🎓 When to Use TAOCP Tools

### ✅ Use TAOCP Tools When:
- You need **exhaustive combinatorial generation** (permutations, combinations, partitions)
- Solving **constraint satisfaction** problems (Sudoku, scheduling, puzzles)
- Performing **cryptographic computations** (modular exponentiation, primality testing)
- **Multi-pattern search** in large texts (DNA sequences, virus scanning)
- **Specialized graph algorithms** (bipartite matching, max flow, SCC)
- **Symbolic mathematics** (differentiation, simplification)

### ❌ Use Python Stdlib When:
- Basic sorting (`sorted()`, `list.sort()`)
- Basic searching (`bisect`, `in` operator)
- Simple randomization (`random.shuffle`, `random.sample`)
- Basic math (`math.factorial`, `math.comb`)

---

## 🤝 Contributing

Contributions welcome! Please:

1. Fork the repository
2. Create a feature branch (`git checkout -b feature/amazing-feature`)
3. Commit your changes (`git commit -m 'Add amazing feature'`)
4. Push to the branch (`git push origin feature/amazing-feature`)
5. Open a Pull Request

### Development Setup

```bash
git clone https://github.com/ksjpswaroop/algorithmic-ai-mcp.git
cd algorithmic-ai-mcp
pip install -e ".[dev]"
pre-commit install
```

---

## 📄 License

Distributed under the MIT License. See [LICENSE](LICENSE) for more information.

---

## 🙏 Acknowledgments

- **Donald Knuth** for The Art of Computer Programming — the foundation of this library
- **TAOCP SDK** — Core algorithm implementations
- **Hermes-Agent** — Primary integration target and testing ground
- **MCP Foundation** — Model Context Protocol for agent tool standardization

---

## 📬 Contact

- **Author:** Swaroop (ksjpswaroop@gmail.com)
- **Repository:** https://github.com/ksjpswaroop/algorithmic-ai-mcp
- **TAOCP SDK:** https://github.com/ksjpswaroop/taocp-complete

---

## 🚀 Roadmap

### v1.0 (MVP) — Q4 2026
- ✅ 15 Tier 1 tools implemented
- ✅ Safety guards on all tools
- ✅ Integration tests with >90% accuracy
- ⏳ PyPI publication
- ⏳ MCP server packaging

### v1.1 — Q1 2027
- String analysis tools (Aho-Corasick, suffix trees, BWT)
- Graph specialized tools (matching, flow, SCC)
- Symbolic math tools (differentiation, simplification)
- Documentation site

### v2.0 — Q2 2027
- Tier 2 internal utilities
- Advanced routing (ML-based tool selection)
- Caching layer for repeated computations
- Rate limiting for shared deployments
- Streaming outputs for large generators

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**Built with ❤️ for the AI agent ecosystem**