Introducing The Maximum Common Bigraph Problem

2026-01-07

Electronic Proceedings in Theoretical Computer Science

AI Summary

This work addresses the absence of efficient algorithms for computing the maximal shared structure between two bigraphs, a limitation that has hindered bisimulation verification in bigraph-based formalisms. We formally define the Maximum Common Bigraph problem for the first time and extend the McSplit algorithm—originally designed for maximum common induced subgraphs—to the domain of bigraphs, effectively accommodating their nodes, edges, and nested region structures. The proposed method constitutes the first algorithm capable of computing the maximal common structure between bigraphs, thereby providing essential support for bisimulation checking. By bridging the gap between bigraph theory and practical tooling, this approach lays a foundational groundwork for modeling, optimization, and formal verification in systems governed by bigraphical representations.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic 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
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

Bigraph reactive systems offer a powerful and flexible mathematical framework for modelling both spatial and non-spatial relationships between agents, with practical applications in domains such as smart technologies, networks, sensor systems, and biology. While bigraphs theoretically support the identification of bisimilar agents, by simulating and comparing their corresponding minimal contextual transition systems, no known algorithm exists for computing the maximum shared structure between two bigraphs, an essential prerequisite for determining the set of possible transitions for a given agent state. In this work, we provide a definition of the maximum common bigraph problem, and present an adaptation of the McSplit maximum common induced subgraph algorithm to compute the maximum common bigraph between two bigraph states. Our approach opens a path toward supporting bisimulation checking in bigraph-based tools, which have been leveraged in other modelling paradigms for simplification, optimisation, and verification of models.

Problem

• maximum common bigraph
• bigraph reactive systems
• bisimulation
• contextual transition systems
• induced subgraph

Innovation

• maximum common bigraph
• bigraph reactive systems
• bisimulation
• McSplit algorithm
• contextual transition systems