Rate-Distortion for Reversible Causal Nets under Closure-Preserving Fidelity

2026-06-15

AI Summary

This study addresses the challenge of log compression in reversible causal nets, balancing semantic fidelity with compression efficiency. The authors propose a semantic rate-distortion theory that characterizes rollback-relevant semantics via monotonic semantic closures and introduces a closure-preserving fidelity criterion. By decomposing logs into an irreducible core and redundant components, only the core is encoded to achieve high compression efficiency. The work innovatively incorporates a closure-preserving distortion measure and a canonical deletion-scan mechanism, extending the classical information-theoretic rate-distortion framework to reversible concurrent models for the first time. A confusion hypergraph is employed to characterize the minimal coding rate required for zero-distortion reconstruction. Experiments across diverse reversible causal nets and prime event structures validate the theoretical predictions, demonstrating significantly improved compression performance while rigorously preserving semantic consistency.

Abstract

We develop a semantic rate-distortion theory for reversible logging under a closure-preserving fidelity criterion. An execution history is modeled as a finite set of logged facts, and rollback-relevant meaning is captured by a monotone semantic closure induced by an effective rule system such as Datalog. We introduce a bounded distortion that edits one logged fact and measures the resulting change in closure. A canonical deletion scan decomposes the log into an irredundant core and a redundant remainder; under admissible reconstructions, redundant facts become information-theoretically invisible, yielding a core-only rate-distortion reduction. At perfect fidelity, overlaps among zero-distortion reconstructions induce a confusability hypergraph that determines the minimum rate. We instantiate the framework on reversible causal nets and reversible prime event structures under multiple reversing disciplines, and validate the predictions numerically.

Problem

• rate-distortion
• reversible causal nets
• closure-preserving fidelity
• semantic compression
• execution logging

Innovation

• rate-distortion
• reversible causal nets
• closure-preserving fidelity
• semantic closure
• confusability hypergraph