Reversify any sequential algorithm

TL;DR

This paper presents a method to transform any sequential algorithm into a step-by-step reversible version by adding bookkeeping, enabling exact reversal of the original algorithm's execution.

Contribution

It introduces a practical approach to reversify arbitrary sequential algorithms using instrumentation, building on theoretical foundations of abstract state machines.

Findings

Reversible algorithms can be constructed from any sequential algorithm.

The method preserves the original algorithm's behavior exactly.

The approach is practical and grounded in established theoretical models.

Abstract

To reversify an arbitrary sequential algorithm $A$, we gently instrument $A$ with bookkeeping machinery. The result is a step-for-step reversible algorithm that mimics $A$ step-for-step and stops exactly when $A$ does. Without loss of generality, we presume that algorithm $A$ is presented as an abstract state machine that is behaviorally identical to $A$. The existence of such representation has been proven theoretically, and the practicality of such representation has been amply demonstrated.