Effectful Mealy Machines: Bisimulation and Trace

2024-10-14

arXiv.org

AI Summary

This paper addresses the lack of semantic uniformity and difficulties in comparing similarity and functionality when modeling causal interactive systems with Mealy machines. To resolve these issues, we propose a Mealy machine model augmented with global effects. Our approach introduces free consistent feedback to syntactically characterize bisimilarity and constructs a coinductive trace semantics universe based on effect flows. We establish, for the first time, a unified bisimulation–trace semantics framework for effect-enhanced Mealy machines, reconciling syntactic characterization with coinductive modeling. Theoretically, we prove that this framework fully generalizes standard causal processes, precisely subsumes classical Mealy machines and their variants, and strictly captures both their bisimulation relations and trace semantics. Consequently, it provides a verifiable and extensible semantic foundation for effectful interactive systems.

Technology Category

• Machine Learning: Causal Learning
• Knowledge Representation and Reasoning: Action, Change, and Causality
• Multiagent Systems: Mechanism Design

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

We introduce effectful Mealy machines - a general notion of Mealy machine with global effects - and give them semantics in terms of both bisimilarity and traces. Bisimilarity of effectful Mealy machines is characterized syntactically, via free uniform feedback. Traces of effectful Mealy machines are given a novel semantic coinductive universe in terms of effectful streams. We prove that this framework generalizes standard causal processes and captures existing flavours of Mealy machine, bisimilarity, and trace.

Problem

• Meli Machine
• Similarity Comparison
• System Impact

Innovation

• Effective Meli Machine
• Dual Similarity Analysis
• Function Tracing Methodology