Given two algorithms for the same problem, can we determine whether they are meaningfully different? In full generality, the question is uncomputable, and empirically it is muddied by competing notions of similarity. Yet, in many applications (such as clone detection or program synthesis) a pragmatic and consistent similarity metric is necessary. We review existing equivalence and similarity notions and introduce EMOC: An Evaluation-Memory-Operations-Complexity framework that embeds algorithm implementations into a feature space suitable for downstream tasks. We compile PACD, a curated dataset of verified Python implementations across three problems, and show that EMOC features support clustering and classification of algorithm types, detection of near-duplicates, and quantification of diversity in LLM-generated programs. Code, data, and utilities for computing EMOC embeddings are released to facilitate reproducibility and future work on algorithm similarity.

翻译：给定针对同一问题的两种算法，我们能否判断它们是否存在本质差异？在完全一般性下，该问题是不可计算的，且实证研究中常因相似性概念的相互竞争而模糊不清。然而，在许多应用场景（如代码克隆检测或程序合成）中，需要一种实用且一致的相似性度量标准。本文系统梳理了现有的等价性与相似性概念，并提出了EMOC框架：一种基于评估-内存-操作-复杂度的特征空间嵌入方法，可将算法实现映射至适用于下游任务的特征空间。我们构建了PACD数据集，这是一个涵盖三类问题的已验证Python实现精选数据集，并证明EMOC特征能够支持算法类型的聚类与分类、近似重复代码的检测，以及大语言模型生成程序多样性的量化分析。为促进算法相似性研究的可复现性与后续工作，我们已公开计算EMOC嵌入向量的代码、数据及相关工具。