Mcp Solver

What is Mcp Solver about?

Mcp Solver is a Model Context Protocol (MCP) server that bridges large language models (LLMs) with constraint‑solving technologies. It supports SAT, MaxSAT, SMT and MiniZinc models, allowing an LLM to manipulate a formal model step‑by‑step (clear, add, delete, replace items) and request a solution with optional timeout.

How to use Mcp Solver?

1. Clone the repository

   git clone https://github.com/szeider/mcp-solver.git
   cd mcp-solver
   

2. Create a virtual environment with uv

   uv venv
   source .venv/bin/activate
   

3. Install the desired backends (choose one or all)

   uv pip install -e "[mzn]"   # MiniZinc mode
   uv pip install -e "[pysat]" # PySAT / MaxSAT mode
   uv pip install -e "[z3]"    # Z3 mode
   uv pip install -e "[all]"   # all solvers
   

4. Start the server using the mode‑specific entry point:
   • MiniZinc: mcp-solver-mzn
   • PySAT: mcp-solver-pysat
   • MaxSAT: mcp-solver-maxsat
   • Z3: mcp-solver-z3
5. Interact via the MCP client (optional) for testing:

   uv pip install -e "[client]"
   uv run run-test mzn --problem path/to/problem.md   # example for MiniZinc
   

   The client requires an LLM API key (e.g., ANTHROPIC_API_KEY).

Key features of Mcp Solver

• Four backend modes: MiniZinc (with Chuffed), PySAT, MaxSAT (RC2), Z3 SMT.
• Toolset for model manipulation: clear_model, add_item, delete_item, replace_item, get_model, solve_model.
• Timeout support for solving requests.
• Optimization capabilities in MiniZinc, MaxSAT and Z3 modes.
• Cross‑platform: works on macOS, Windows and Linux.
• LLM‑ready client based on the ReAct framework for end‑to‑end interaction.

Use cases of Mcp Solver

• Automated puzzle solving (e.g., N‑Queens, casting problems) driven by natural‑language prompts.
• Planning and routing (e.g., traveling salesperson) where an LLM generates the model and retrieves the optimal route.
• Verification of logical specifications by letting the LLM encode constraints and ask the server to check satisfiability.
• Educational tooling for teaching constraint programming through conversational interfaces.
• Prototype AI assistants that need to reason about combinatorial problems without implementing solvers themselves.

FAQ from the Mcp Solver

Q: Which Python version is required? A: Python 3.11 or newer.

Q: Do I need to install MiniZinc or Z3 separately? A: The required packages are pulled via pip (minizinc, z3‑solver). MiniZinc also needs the MiniZinc command‑line tools installed on the system.

Q: Can I run multiple backends simultaneously? A: Each backend runs as a separate executable (e.g., mcp-solver-mzn). You can start several instances on different ports.

Q: How do I set a solving timeout? A: Pass a timeout parameter to the solve_model tool; the server forwards it to the underlying solver.

Q: Is the project production‑ready? A: It is a prototype; suitable for experimentation and research but should be used with caution in critical environments.

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MCP Solver

A Model Context Protocol (MCP) server that exposes SAT, SMT and constraint solving capabilities to Large Language Models.

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Overview

The MCP Solver integrates SAT, SMT and Constraint Solving with LLMs through the Model Context Protocol, enabling AI models to interactively create, edit, and solve:

• Constraint models in MiniZinc
• SAT models in PySAT
• MaxSAT optimization problems in PySAT
• SMT formulas in Z3 Python

For a detailed description of the MCP Solver's system architecture and theoretical foundations, see the accompanying research paper: Stefan Szeider, "MCP-Solver: Integrating Language Models with Constraint Programming Systems", arXiv:2501.00539, 2024.

Available Tools

In the following, item refers to some part of the (MinZinc/Pysat/Z3) code, and model to the encoding.

Tool Name	Description
clear_model	Remove all items from the model
add_item	Add new item at a specific index
delete_item	Delete item at index
replace_item	Replace item at index
get_model	Get current model content with numbered items
solve_model	Solve the model (with timeout parameter)

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System Requirements

• Python and project manager uv
• Python 3.11+
• Mode-specific requirements: MiniZinc, PySAT, Python Z3 (required packages are installed via pip)
• Operating systems: macOS, Windows, Linux (with appropriate adaptations)

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Installation

MCP Solver requires Python 3.11+, the uv package manager, and solver-specific dependencies (MiniZinc, Z3, or PySAT).

For detailed installation instructions for Windows, macOS, and Linux, see INSTALL.md.

Quick start:

git clone https://github.com/szeider/mcp-solver.git
cd mcp-solver
uv venv
source .venv/bin/activate
uv pip install -e ".[all]"  # Install all solvers

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Available Modes / Solving Backends

The MCP Solver provides four distinct operational modes, each integrating with a different constraint solving backend. Each mode requires specific dependencies and offers unique capabilities for addressing different classes of problems.

MiniZinc Mode

MiniZinc mode provides integration with the MiniZinc constraint modeling language with the following features:

• Rich constraint expression with global constraints
• Integration with the Chuffed constraint solver
• Optimization capabilities
• Access to solution values via get_solution

Dependencies: Requires the minizinc package (uv pip install -e ".[mzn]")

Configuration: To run in MiniZinc mode, use:

mcp-solver-mzn

PySAT Mode

PySAT mode allows interaction with the Python SAT solving toolkit with the following features:

• Propositional constraint modeling using CNF (Conjunctive Normal Form)
• Access to various SAT solvers (Glucose3, Glucose4, Lingeling, etc.)
• Cardinality constraints (at_most_k, at_least_k, exactly_k)
• Support for boolean constraint solving

Dependencies: Requires the python-sat package (uv pip install -e ".[pysat]")

Configuration: To run in PySAT mode, use:

mcp-solver-pysat

MaxSAT Mode

MaxSAT mode provides specialized support for optimization problems with PySAT, featuring:

• Weighted Conjunctive Normal Form (WCNF) support
• Integration with the RC2 MaxSAT solver
• Optimization capabilities with objective tracking
• Support for both hard and soft constraints

Dependencies: Requires the python-sat package (uv pip install -e ".[pysat]")

Configuration: To run in MaxSAT mode, use:

mcp-solver-maxsat

Z3 Mode

Z3 mode provides access to Z3 SMT (Satisfiability Modulo Theories) solving capabilities with the following features:

• Rich type system: booleans, integers, reals, bitvectors, arrays
• Constraint solving with quantifiers
• Optimization capabilities
• Template library for common modeling patterns

Dependencies: Requires the z3-solver package (uv pip install -e ".[z3]")

Configuration: To run in Z3 mode, use:

mcp-solver-z3

MCP Test Client

The MCP Solver includes an MCP client for development, experimentation, and diagnostic purposes, based on the ReAct agent framework. This client serves as an intermediary between an LLM and the MCP server, facilitating the translation of natural language problem statements into formal constraint programming solutions.

Installation

# Install client dependencies
uv pip install -e ".[client]"

# Verify client installation and configuration
uv run test-setup-client

The client requires an API key from an LLM provider. For Anthropic (the default LLM is Claude Sonnet 3.7), set the ANTHROPIC_API_KEY environment variable. This can be set in your environment or included in a .env file in the project root.

The client also supports other LLM providers including OpenAI, Google (Gemini), OpenRouter, and even local models via LM Studio. You can specify which model to use with the --mc command line flag. See INSTALL.md for details on model code formats.

Usage

The client provides specialized commands for each solver backend:

# MiniZinc mode
uv run run-test mzn --problem <path/to/problem.md>

# PySAT mode
uv run run-test pysat --problem <path/to/problem.md>

# MaxSAT mode
uv run run-test maxsat --problem <path/to/problem.md>

# Z3 mode
uv run run-test z3 --problem <path/to/problem.md>

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Examples

Example 1: Casting Problem (MiniZinc)

This is based on an example by George Johnson (NYT, July 13, 1999).

User

Suppose that a theatrical director feels obligated to cast either his ingenue, Actress Alvarez, or his nephew, Actor Cohen, in a production. But Miss Alvarez won't be in a play with Mr. Cohen (her former lover), and she demands that the cast include her new flame, Actor Davenport. The producer, with her own favors to repay, insists that Actor Branislavsky have a part. But Mr. Branislavsky won't be in any play with Miss Alvarez or Mr. Davenport. Can the director cast the play?

System: clear_model

Model cleared

System: add_item (multiple)

var bool: alvarez;
var bool: cohen;
var bool: branislavsky;
var bool: davenport;
constraint alvarez \/ cohen;                          % Must cast either Alvarez or Cohen
constraint not (alvarez /\ cohen);                    % Alvarez won't work with Cohen
constraint alvarez -> davenport;                      % If Alvarez is cast, Davenport must be cast
constraint branislavsky;                              % Branislavsky must be cast
constraint not (branislavsky /\ alvarez);             % Branislavsky won't work with Alvarez
constraint not (branislavsky /\ davenport);           % Branislavsky won't work with Davenport
solve satisfy;

System: solve_model

{'status': 'SAT', 'solution': Solution(alvarez=False, cohen=True, branislavsky=True, davenport=False, _checker=''), 'solve_time': 0.0}

The solution (cast Cohen and Branislavsky, but not Alvarez or Davenport) satisfies all constraints.

Example 2: N-Queens Problem (MiniZinc)

User

Check whether you can place n Queens on an nxn chessboard. Try n=10,20,30,40 and compare the solving times

System: clear_model

Model cleared

System: add_item (multiple)

int: n = 10;
array[1..n] of var 1..n: queens;
constraint alldifferent(queens);
constraint alldifferent([queens[i] + i | i in 1..n]);
constraint alldifferent([queens[i] - i | i in 1..n]);
solve satisfy;

System: solve_model (with n=10, 20, 30, and 40 by changing the value of n)

Solve times comparison: n=10: 0.001s n=20: 0.005s n=30: 0.040s n=40: 0.043s

Solutions exist for all tested board sizes. Time complexity increases non-linearly but remains manageable up to n=40.

Example 3: Traveling Salesperson Problem (MiniZinc)

User

A saleswoman based in Vienna needs to plan her upcoming tour through Austria, visiting each province capital once. Help find the shortest route. Distances in km: 1=Vienna, 2=St. Pölten, 3=Eisenstadt, 4=Linz, 5=Graz, 6=Klagenfurt, 7=Salzburg, 8=Innsbruck, 9=Bregenz

[Distance matrix table provided in user message]

System: add_item (multiple)

include "globals.mzn";
int: n = 9;
array[1..n,1..n] of int: dist = [|0,65,60,184,195,319,299,478,631|65,0,125,119,130,254,234,413,566|60,125,0,184,157,281,261,440,593|184,119,184,0,208,252,136,315,468|195,130,157,208,0,136,280,459,629|319,254,281,252,136,0,217,391,566|299,234,261,136,280,217,0,188,343|478,413,440,315,459,391,188,0,157|631,566,593,468,629,566,343,157,0|];
array[1..n] of var 1..n: succ;
var int: total_dist = sum(i in 1..n)(dist[i,succ[i]]);
constraint circuit(succ);
solve minimize total_dist;

System: solve_model

{'status': 'SAT', 'solution': Solution(objective=1564, succ=[2, 4, 1, 7, 3, 5, 9, 6, 8], _checker=''), 'solve_time': 0.002}

Optimal route: Vienna → St. Pölten → Linz → Salzburg → Bregenz → Innsbruck → Klagenfurt → Graz → Eisenstadt → Vienna with a total distance of 1,564 km.

Feedback

You can provide feedback to the author via this form.

Disclaimer

This MCP Solver is in its prototype stage and should be used with caution. Users are encouraged to experiment, but any use in critical environments is at their own risk.

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License

This project is licensed under the MIT License - see the LICENSE file for details.

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