🤖 AI Summary
This work addresses the challenge of efficiently verifying whether concurrency control protocols satisfy serializability semantics. The authors propose CV-Rules, a novel method that decomposes serializability into two orthogonal conditions: causality (C-rules) and view consistency (V-rules), enabling explicit construction of transaction orders and overcoming limitations of traditional multi-version serialization graph techniques. Under bounded causal width, CV-Rules permits polynomial-time decidability and, for the first time, yields explicit transaction orders for several protocols. Implemented within the Lean theorem prover, the formal verification requires no additional axioms and successfully verifies Two-Phase Locking, MVTO, SSN, Aria, and SnapChain. The analysis further reveals that Aria’s unique-write constraint is unnecessary and demonstrates that SnapChain natively satisfies V-rules.
📝 Abstract
We present CV-rules, an alternative characterization of serializability in which a transaction order constructed by a protocol satisfies two per-read conditions, C-rule (Causality) and V-rule (View Consistency), that constrain the reads-from relation and competing writers. While classical Multi-Version Serialization Graph (MVSG) reasoning characterizes serializability via its acyclicity, our approach requires explicit order construction, enabling direct proofs that build on the protocol's own mechanisms. We prove that CV-rules, serializability, and MVSG acyclicity are all equivalent. Moreover, the C/V separation reveals that serializability is polynomial-time decidable for any fixed bound on the width of the order forced by C-rule. We verify five protocols: Two-Phase Locking, Multi-Version Timestamp Ordering, Serial Safety Net (SSN), Aria, and SnapChain. For SSN and Aria, whose original papers defined only certification conditions, we identify explicit transaction orders arising from their mechanisms; we also prove that Aria's unique-write constraint is unnecessary for serializability. SnapChain, in contrast, is designed directly from CV-rules, enforcing V-rule by construction. All results except the complexity bounds are mechanized in Lean with no additional axioms and no admitted goals.