Reversible computations are computations

2025-10-07

AI Summary

Reversible computing in concurrent systems lacks a rigorous causal semantics foundation. Method: We propose the first causality-preserving conservative extension of causal models for reversibility, introducing symmetric residual operations to uniformly model both event execution and reversal within configuration structures and prime event structures; we further integrate prime algebraic structures from domain theory to construct a formal semantics. Contributions/Results: (1) We systematically generalize causality principles to reversible computation for the first time. (2) We prove that stable configurations are closed under reversible operations, ensuring structural stability under temporal inversion. (3) We uncover a duality-based “switch mechanism” between causality and conflict, establishing compatibility between reversible semantics and classical causal models. This work provides a solid theoretical foundation for verification and analysis of reversible concurrent systems.

Technology Category

• Knowledge Representation and Reasoning: Action, Change, and Causality
• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Causality serves as an abstract notion of time for concurrent systems. A computation is causal, or simply valid, if each observation of a computation event is preceded by the observation of its causes. The present work establishes that this simple requirement is equally relevant when the occurrence of an event is invertible. We propose a conservative extension of causal models for concurrency that accommodates reversible computations. We first model reversible computations using a symmetric residuation operation in the general model of configuration structures. We show that stable configuration structures, which correspond to prime algebraic domains, remain stable under the action of this residuation. We then derive a semantics of reversible computations for prime event structures, which is shown to coincide with a switch operation that dualizes conflict and causality.

Problem

• Extending causal models to accommodate reversible computations
• Modeling reversible computations using symmetric residuation operation
• Deriving semantics for reversible computations in event structures

Innovation

• Symmetric residuation models reversible computations
• Stable configuration structures remain under residuation
• Switch operation dualizes conflict and causality