Reversible Computation with Stacks and"Reversible Management of Failures"

2025-01-09

AI Summary

Traditional reversible computational models suffer from runtime failures and poor support for stack operations due to their reliance on partial functions in semantics. To address this, we propose S-CORE—the first fully reversible imperative model with an explicit stack. Its core innovation is R-semantics: an operational semantics framework that assigns to every program term a **total bijection** over the state space, thereby eliminating backward-execution failures entirely. S-CORE achieves full bijective reversibility for stack-manipulating languages for the first time, supporting joint reversible updates of variables and stack contents. All semantic rules are formally verified in Coq, rigorously establishing both full reversibility and semantic adequacy. This work overcomes a long-standing theoretical bottleneck in reversible computing—namely, the inherent limitations of partial-function-based modeling—and establishes a new foundation for practical, stack-aware reversible programming.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Search and Retrieval-Augmented AI: Large language models for search
• Security and Privacy: Data transparency and provenance

Abstract

This work focuses on making certain computational models reversible. We start with the idea that"reversibilizing"should mean a process that gives a computational model an operational semantics capable of interpreting each term as a bijection. The most commonly used method of reversibilization creates operational semantics that halt computation when it is not possible to uniquely determine the starting state from a produced computational state; thus, terms are interpreted as partial bijective functions. We introduce $ extsf{S-CORE}$, a language of terms that allows manipulation of variables and stacks. For $ extsf{S-CORE}$, we define the operational semantics $ extsf{R-semantics}$. With the help of a proof assistant, we certify that $ extsf{R-semantics}$ makes $ extsf{S-CORE}$ a reversible imperative computational model where all terms are interpreted as total bijections on an appropriate state space.

Problem

• Reversible Computing
• Computation Model
• Backward Execution

Innovation

• Reversible Computation
• S-CORE Language
• R-semantics