The paper "The Serializability of Concurrent Database Updates" by Christos H. Papadimitriou explores the complexity and properties of serializability in concurrent database systems. The author introduces a simple transaction model where a sequence of interleaved user transactions may not be serializable, meaning they cannot be executed in a sequential order without conflicts. The main findings include: 1. **NP-Completeness**: The problem of determining whether a given sequence of read and write operations (history) is serializable is NP-complete, even when no dead transactions are present. This suggests that there is no efficient algorithm to distinguish between serializable and nonserializable histories. 2. **Efficient Subclasses**: Several efficiently recognizable subclasses of serializable histories are introduced. These include the two-phase locking strategy and the protocol \(P3\), which are shown to be incommensurate special cases of more general classes called \(Q\) and \(DSR\). The class \(SSR\) is also introduced, which allows for serializability without reversing the order of temporally nonoverlapping transactions. 3. **Scheduler Efficiency**: For all efficiently recognizable classes of histories, there exists an efficient scheduler that transforms any given history into its closest equivalent history within the class. This implies that the complexity of recognizing serializable histories is linked to the complexity of scheduling. 4. **Generalizability**: The results can be extended to more general transaction models, transactions with partly interpreted functions, and distributed database systems. 5. **Conclusion**: The paper concludes by discussing possible extensions and implications of the findings, emphasizing the practical relevance of the complexity theory developed in the paper. The paper provides a comprehensive analysis of serializability in concurrent database systems, contributing to the understanding of the theoretical and practical aspects of transaction scheduling and concurrency control.The paper "The Serializability of Concurrent Database Updates" by Christos H. Papadimitriou explores the complexity and properties of serializability in concurrent database systems. The author introduces a simple transaction model where a sequence of interleaved user transactions may not be serializable, meaning they cannot be executed in a sequential order without conflicts. The main findings include: 1. **NP-Completeness**: The problem of determining whether a given sequence of read and write operations (history) is serializable is NP-complete, even when no dead transactions are present. This suggests that there is no efficient algorithm to distinguish between serializable and nonserializable histories. 2. **Efficient Subclasses**: Several efficiently recognizable subclasses of serializable histories are introduced. These include the two-phase locking strategy and the protocol \(P3\), which are shown to be incommensurate special cases of more general classes called \(Q\) and \(DSR\). The class \(SSR\) is also introduced, which allows for serializability without reversing the order of temporally nonoverlapping transactions. 3. **Scheduler Efficiency**: For all efficiently recognizable classes of histories, there exists an efficient scheduler that transforms any given history into its closest equivalent history within the class. This implies that the complexity of recognizing serializable histories is linked to the complexity of scheduling. 4. **Generalizability**: The results can be extended to more general transaction models, transactions with partly interpreted functions, and distributed database systems. 5. **Conclusion**: The paper concludes by discussing possible extensions and implications of the findings, emphasizing the practical relevance of the complexity theory developed in the paper. The paper provides a comprehensive analysis of serializability in concurrent database systems, contributing to the understanding of the theoretical and practical aspects of transaction scheduling and concurrency control.