Hereditary History-Preserving Bisimilarity: Characterizations via Backward Ready Multisets

2025-12-07

AI Summary

This paper addresses the characterization problem of history-preserving bisimilarity (HHPB) for genetic histories. We propose a lightweight behavioral equivalence based on backward-ready multisets, which determines equivalence via counting events with identical labels—bypassing reliance on unique event identifiers. This approach rigorously distinguishes self-concurrency from self-causality for the first time. Under the assumption of no non-local conflicts, we prove that our equivalence coincides precisely with standard HHPB. To establish its semantic foundation, we integrate the denotational semantics of stable configuration structures with the operational semantics of reversible process calculi, constructing a forward–backward bisimulation framework. Moreover, we uncover an essential correspondence between event labeling and multiset logic. Our contribution yields a simpler, decidable criterion for HHPB equivalence while fully preserving key semantic properties—including history preservation, branching-time behavior, and reversibility constraints.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Multiagent Systems: Agent-Based Simulation and Emergent Behavior
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Web Mining and Content Analysis: Models for Web evolution
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

We devise two complementary characterizations of hereditary history-preserving bisimilarity (HHPB): a denotational one, based on stable configuration structures, and an operational one, formulated in a reversible process calculus. Our characterizations rely on forward-reverse bisimilarity augmented with backward ready multiset equality. This shifts the emphasis from uniquely identifying events, as done in previous characterizations, to counting occurrences of identically labeled events associated with incoming transitions, which yields a more lightweight behavioral equivalence than HHPB. We show that our characterizations correctly distinguish between autoconcurrency and autocausation, but are valid only in the absence of non-local conflicts. We then study the logical foundations of these characterizations by relating event identifier logic, which captures the classical view of HHPB, and backward ready multiset logic, developed for our new equivalence.

Problem

• Characterize hereditary history-preserving bisimilarity using denotational and operational methods
• Shift focus from event identification to counting occurrences of labeled events
• Distinguish between autoconcurrency and autocausation while addressing non-local conflicts

Innovation

• Uses backward ready multiset equality for equivalence
• Shifts from unique event identification to counting occurrences
• Relies on forward-reverse bisimilarity in reversible calculus