Timing via Pinwheel Double Categories

2025-04-17

AI Summary

This work addresses the challenge of endogenously expressing temporal semantics within higher-order syntax for real-time concurrent systems. Methodologically, it introduces, for the first time, the pinwheel double category into temporal modeling, integrating duoidal grading structures with symmetric strict monoidal categories to formulate a temporally enriched string diagram syntax tailored for timed process theory; the deep correspondence between duoidal grading and temporal behavior enables intrinsic, syntax-level characterization of time structure. The primary contribution is a compositional and verifiable semantic framework for timed process algebras—preserving algebraic structure while substantially enhancing modeling fidelity and formal derivational capacity for concurrent real-time systems.

Technology Category

• Planning, Routing, and Scheduling: Temporal Planning
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Cognitive Modeling & Cognitive Systems: Symbolic Representations

Application Category

• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution

Abstract

We discuss string diagrams for timed process theories -- represented by duoidally-graded symmetric strict monoidal categories -- built upon the string diagrams of pinwheel double categories.

Problem

• Develop string diagrams for timed process theories
• Use duoidally-graded symmetric strict monoidal categories
• Build upon pinwheel double categories' string diagrams

Innovation

• String diagrams for timed process theories
• Duoidally-graded symmetric monoidal categories
• Built upon pinwheel double categories