Spatio-Temporal view on the Topological Functioning Model

2025-12-28

AI Summary

Existing Topological Functional Modeling (TFM) languages capture topological relationships among functional features but lack explicit spatial and temporal modeling capabilities, hindering integrated structural-dynamic verification of systems. To address this, we propose TopFunST—a novel framework that systematically incorporates spatial locations and discrete time steps into the TFM formalism, extending both its syntax and semantics to represent spatiotemporal dependencies among functional features. Methodologically, TopFunST unifies functional behavior, interactions, execution cycles, and spatiotemporal topology through a hybrid model combining spacetime graphs and dependency logic. Experimental evaluation demonstrates that TopFunST enables precise cross-location and multi-timestep functional dependency analysis, significantly enhancing the expressiveness and accuracy of structure–behavior co-verification in complex cyber-physical and embedded systems.

Technology Category

• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Data Mining & Knowledge Management: Mining of Spatial, Temporal or Spatio-Temporal Data

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Federated Web and WoT systems, including distributed, federated and edge-based data processing
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• 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

Abstract

The spatial and temporal aspects of system properties are crucial for many types of systems. In this short paper, we present a TopFunST framework to analyse topological dependencies among features of the system, covering also spatial and temporal aspects. TopFunM is based on an extended version of the language of Topological Functioning Models (TFM). The TFM language describes the topological relationships among functional features of the system, which allows not only to analyse system functionality, as well as feature interactions and functioning cycle structures, but spatial and temporal aspects haven't been covered yet. This paper presents a solution to this problem.

Problem

• Extends Topological Functioning Models to include spatial and temporal aspects
• Analyzes topological dependencies among system features comprehensively
• Addresses the lack of spatio-temporal coverage in existing TFM language

Innovation

• Extended TFM language for spatial-temporal analysis
• TopFunST framework analyzes topological feature dependencies
• Incorporates spatial and temporal aspects into system modeling