Problem
Research questions and friction points this paper is trying to address.
quantitative co-design
heterogeneous system design
feasibility relations
quantale enrichment
compositional engineering
Quantale-Enriched Co-Design: Toward a Framework for Quantitative Heterogeneous System Design
🤖 AI Summary
Traditional monotone co-design supports only Boolean feasibility checks, making it ill-suited for natively handling quantitative metrics such as cost or confidence, often resorting to ad hoc scalarization or resource-space augmentation that introduces structural ambiguity and computational overhead. This work proposes a quantale-enriched categorical framework for quantitative co-design: resources and functionalities are modeled as quantale-enriched categories, design problems are expressed as quantale-enriched profunctors, and a heterogeneous composition mechanism based on quantale base change is introduced to uniformly integrate feasibility, cost, confidence, and implementation choices. The approach naturally accommodates serial, parallel, and feedback compositions, and experiments in target tracking and drone delivery tasks demonstrate its superior architectural clarity and computational efficiency over conventional Boolean methods.
📝 Abstract
Monotone co-design enables compositional engineering design by modeling components through feasibility relations between required resources and provided functionalities. However, its standard boolean formulation cannot natively represent quantitative criteria such as cost, confidence, or implementation choice. In practice, these quantities are often introduced through ad hoc scalarization or by augmenting the resource space, which obscures system structure and increases computational burden. We address this limitation by developing a quantale-enriched theory of co-design. We model resources and functionalities as quantale-enriched categories and design problems as quantale-enriched profunctors, thereby lifting co-design from boolean feasibility to general quantitative evaluation. We show that the fundamental operations of series, parallel, and feedback composition remain valid over arbitrary commutative quantales. We further introduce heterogeneous composition through change-of-base maps between quantales, enabling different subsystems to be evaluated in different local semantics and then composed in a common framework. The resulting theory unifies feasibility-, cost-, confidence-, and implementation-aware co-design within one compositional formalism. Numerical examples on a target-tracking system and a UAV delivery problem demonstrate the framework and highlight how native quantitative enrichment can avoid the architectural and computational drawbacks of boolean-only formulations.
Innovation
Methods, ideas, or system contributions that make the work stand out.
quantale-enriched co-design
monotone co-design
quantitative system design
heterogeneous composition
enriched category theory
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