$\texttt{codesign-mcdp}$: A Python Library for Monotone Co-Design Problems

2026-07-20

AI Summary

This work presents the first systematic implementation for monotone co-design problems (MCDPs)—formulated as finding the minimal resource antichain satisfying given functional requirements. Building upon Censi’s (2015) theoretical framework, the authors develop an open-source Python library that supports serial, parallel, and feedback composition operators, offering a declarative and modular modeling interface. The implementation innovatively integrates poset theory, antichain calculus, and Kleene fixed-point algorithms, and extends the framework to handle uncertainty modeling, online learning, and dynamic-state co-design. The library includes six fundamental problem types, composition operators, solvers, and extensive examples, demonstrating the approach’s effectiveness and scalability across multiple domains.

Abstract

$\texttt{codesign-mcdp}$ is a Python library for formulating and solving $\textit{Monotone Co-Design Problems}$ (MCDPs) in the framework of Censi (2015). A design problem is a relation between two posets, a functionality poset $F$ and a resource poset $R$; given a target functionality, the problem asks for the antichain of minimal resources needed to deliver it. Design problems compose under three operators (series, parallel, feedback), and the resulting class is closed under composition. The library implements the antichain calculus, six primitive design-problem types, the three composition operators, a Kleene fixed-point solver, and two high-level builders (an MCDPL-style declarative builder and a modular $\texttt{System}$ builder). Further layers add set-based and stochastic uncertainty, compositional online learning, and temporal, vector-state, and online co-design, alongside a suite of worked examples.

Problem

• Monotone Co-Design Problems
• antichain
• poset
• resource allocation
• functionality

Innovation

• Monotone Co-Design Problems
• antichain calculus
• compositional design
• Kleene fixed-point solver
• uncertainty-aware co-design