This paper discusses the challenges and requirements of concurrency control in real-time groupware systems, which support multiple users engaged in a common task and require fine-granularity data sharing and fast response times. The authors distinguish real-time groupware from other multi-user systems and present an algorithm for concurrency control that is simple to use and responsive, allowing users to operate directly on data without obtaining locks. The algorithm's structure is independent of semantic information, making it adaptable to various scenarios. An example application to group text editing is provided, along with a sketch of its correctness proof. The paper also highlights the non-serializable behavior often desired in such systems. The authors conclude by discussing the implications of their work and future directions, including generalizing the transform matrix and extending the proof technique to other groupware systems.This paper discusses the challenges and requirements of concurrency control in real-time groupware systems, which support multiple users engaged in a common task and require fine-granularity data sharing and fast response times. The authors distinguish real-time groupware from other multi-user systems and present an algorithm for concurrency control that is simple to use and responsive, allowing users to operate directly on data without obtaining locks. The algorithm's structure is independent of semantic information, making it adaptable to various scenarios. An example application to group text editing is provided, along with a sketch of its correctness proof. The paper also highlights the non-serializable behavior often desired in such systems. The authors conclude by discussing the implications of their work and future directions, including generalizing the transform matrix and extending the proof technique to other groupware systems.