On the Correctness Problem for Serializability

• Published in: Theoretical Aspects of Computing - ICTAC 2021 Vol. 12819; pp. 47 - 64
• Main Authors: König, Jürgen, Wehrheim, Heike
• Format: Book Chapter
• Language: English
• Published: Switzerland Springer International Publishing AG 2021; Springer International Publishing
• Series: Lecture Notes in Computer Science
• ISBN: 3030853144; 9783030853143
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-030-85315-0_4

Concurrent correctness conditions formalize the notion of “seeming atomicity” in concurrent access to shared object state. For different sorts of objects (databases, concurrent data structures, software transactional memory) different sorts of correctness conditions have been proposed (serializability, linearizability, opacity). Decidability of concurrent correctness conditions studies two problems: the membership problem asks whether a single execution is correct; the correctness problem asks whether all executions of a given implementation are correct. In this paper we investigate decidability of Papadimitrious’s notion of serializability for database transactions. Papadimitriou has proved the membership problem for serializability to be NP-complete. For correctness we consider a stricter version also proposed by Papadimitriou, which requires an additional real time order constraint. We show this version to be decidable given that all transactions are live.