# Correct and Efficient Antichain Algorithms for Refinement Checking

## TL;DR

This paper introduces corrected and more efficient antichain algorithms for refinement checking in software systems, improving performance and correctness over previous methods through experimental validation.

## Contribution

It presents new, sound antichain algorithms for refinement checking and demonstrates their superior efficiency compared to earlier algorithms.

## Key findings

- Algorithms outperform original ones in runtime
- Algorithms use less memory
- Additional improvements via divergence-preserving minimisation

## Abstract

The notion of refinement plays an important role in software engineering. It is the basis of a stepwise development methodology in which the correctness of a system can be established by proving, or computing, that a system refines its specification. Wang et al. describe algorithms based on antichains for efficiently deciding trace refinement, stable failures refinement and failures-divergences refinement. We identify several issues pertaining to the soundness and performance in these algorithms and propose new, correct, antichain-based algorithms. Using a number of experiments we show that our algorithms outperform the original ones in terms of running time and memory usage. Furthermore, we show that additional run time improvements can be obtained by applying divergence-preserving branching bisimulation minimisation.