Algorithmic AI MCP — TAOCP Agent Tools

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).

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🎯 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

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🚀 Quick Start

Installation

pip install taocp-agent-tools

Basic Usage

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}")

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📦 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

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🛡️ Safety Features

Combinatorial Explosion Prevention

# 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

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

Input Validation

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

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🔌 MCP Server (Coming Soon)

Make TAOCP tools available to any MCP-compatible agent:

# Install MCP server
pip install taocp-agent-mcp

# Run server
taocp-mcp-server

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

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📊 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

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🧪 Testing

# 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

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📚 Documentation

• PRD — Complete 39-section Product Requirements Document
• Status Report — Implementation status, metrics, next steps
• API Reference — Full API documentation (auto-generated)

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🏗️ 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

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🎓 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)

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🤝 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

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

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📄 License

Distributed under the MIT License. See LICENSE for more information.

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🙏 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

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📬 Contact

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

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🚀 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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