Complex Systems were identified and studied in different fields, such as physics, biology, and economics. These systems exhibit exciting properties such as self-organization, robust order, and emergence. In recent years, software systems displaying behaviors associated with Complex Systems are starting to appear, and these behaviors are showing previously unknown potential (e.g., GPT-based applications). Yet, there is no commonly shared definition of a Complex Software System that can serve as a key reference for academia to support research in the area. In this paper, we adopt the theory-to-research strategy to extract properties of Complex Systems from research in other fields, mapping them to software systems to create a formal definition of a Complex Software System. We support the evolution of the properties through future validation, and we provide examples of the application of the definition. Overall, the definition will allow for a more precise, consistent, and rigorous frame of reference for conducting scientific research on software systems.

翻译：复杂系统已在物理学、生物学和经济学等不同领域被识别和研究。这些系统展现出令人振奋的特性，如自组织、鲁棒有序性和涌现性。近年来，开始出现呈现复杂系统相关行为的软件系统，这些行为展现出前所未有的潜力（例如基于GPT的应用）。然而，目前尚缺乏一个被广泛认可的复杂软件系统定义，作为学术界支持该领域研究的关键参考。本文采用"理论-研究"策略，从其他领域的研究中提取复杂系统的特性，并将其映射到软件系统，从而形成复杂软件系统的形式化定义。我们通过未来验证支持这些特性的演进，并提供定义应用的示例。总体而言，该定义将为软件系统科学研究提供更精确、一致且严谨的参考框架。