Conformance Games for Graded Semantics

2024-11-05

arXiv.org

AI Summary

This paper addresses the lack of a unified quantitative framework for program behavior similarity and conformance. Methodologically, it introduces a general conformance theory grounded in category theory and topological game semantics: behavioral conformance—encompassing trace inclusion, probabilistic trace distance, and simulation distance—is abstracted as structured objects within a topological category, yielding a unified game-based framework that subsumes equivalence, preorders, and pseudometrics, and applies to probabilistic, weighted, and game-based branching systems. Contributions include: (i) a sound and complete generic game characterization, overcoming the limitations of traditional binary equivalences; (ii) instantiation and reconstruction of classical semantics—including bisimulation topology and simulation distance for transition systems—and support for non-relational system modeling. The framework provides a formal foundation for program verification, robustness analysis, and cross-paradigm behavioral comparison.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning
• Game Theory and Economic Paradigms: Behavioral Game Theory

Application Category

• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• 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: Web performance, measurement, and characterization

Abstract

Game-theoretic characterizations of process equivalences traditionally form a central topic in concurrency; for example, most equivalences on the classical linear-time / branching-time spectrum come with such characterizations. Recent work on so-called graded semantics has led to a generic behavioural equivalence game that covers the mentioned games on the linear-time~/ branching-time spectrum and moreover applies in coalgebraic generality, and thus instantiates also to equivalence games on systems with non-relational branching type (probabilistic, weighted, game-based etc.). In the present work, we generalize this approach to cover other types of process comparison beyond equivalence, such as behavioural preorders or pseudometrics. At the most general level, we abstract such notions of behavoiural conformance in terms of topological categories, and later specialize to conformances presented as relational structures to obtain a concrete syntax. We obtain a sound and complete generic game for behavioural conformances in this sense. We present a number of instantiations, obtaining game characterizations of, e.g., trace inclusion, probabilistic trace distance, bisimulation topologies, and simulation distances on metric labelled transition systems.

Problem

• Behavioral Similarity
• Computer Programs
• Probabilistic Analysis

Innovation

• Behavioral Similarity
• Universal Method
• Probabilistic and Weighted Programs