Technology Category
Planning, Routing, and Scheduling: Temporal PlanningKnowledge Representation and Reasoning: Geometric, Spatial, and Temporal ReasoningCognitive Modeling & Cognitive Systems: Symbolic Representations
Timing via Pinwheel Double Categories
🤖 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
Application Category
📝 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
Research questions and friction points this paper is trying to address.
Develop string diagrams for timed process theories
Use duoidally-graded symmetric strict monoidal categories
Build upon pinwheel double categories' string diagrams
Innovation
Methods, ideas, or system contributions that make the work stand out.
String diagrams for timed process theories
Duoidally-graded symmetric monoidal categories
Built upon pinwheel double categories
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