Automatic Verification of Sequential Consistency for Unbounded Addresses and Data Values

Abstract

Sequential consistency is the archetypal correctness condition for the memory protocols of shared-memory multiprocessors. Typically, such protocols are parameterized by the number of processors, the number of addresses, and the number of distinguishable data values, and typically, automatic protocol verification analyzes only concrete instances of the protocol with small values (generally < 3) for the protocol parameters. This paper presents a fully automatic method for proving the sequential consistency of an entire parameterized family of protocols, with the number of processors fixed, but the number of addresses and data values being unbounded parameters. Using some practical, reasonable assumptions (data independence, processor symmetry, location symmetry, simple store ordering, some syntactic restrictions), the method automatically generates a finite-state abstract protocol from the parameterized protocol description; proving sequential consistency of the abstract model, via known methods, guarantees sequential consistency of the entire protocol family. The method is sound, but incomplete, but we argue that it is likely to apply to most real protocols. We present experimental results showing the effectiveness of our method on parameterized versions of the Piranha shared memory protocol and an extended version of a directory protocol from the University of Wisconsin Multifacet Project.

On the Complexity of Checking Consistency for Replicated Data Types

“…While Bouajjani et al [5,14] consider the complexity for individual linearizable collection types, we are the first to establish (in)tractability of individual replicated data types. Others have developed effective consistency checking algorithms for sequential consistency [3,9,23,31], serializability [12,17,18,21], linearizability [10,16,28,37], and even weaker notions like eventual consistency [7] and sequential happens-before consistency [13,15]. In contrast, we are the first to establish precise polynomial-time algorithms for runtime verification of replicated data types.…”

“…In a practical context, this can be enforced by tagging characters with replica identifiers and sequence numbers 3. This element is not returned by read operations.…”

Verifying Concurrent Programs against Sequential Specifications

“…Several works have also developed techniques for verifying sequential consistency [20,29,5,8] and serializability [12,30,17,19,15]; Farzan and Madhusudan [17] demonstrate a complete technique for verifying conflict serializability with a bounded number of concurrent operations, and while Guerraoui et al [19] identify symmetry conditions on transactional systems with which conflict serializability can be verified completely, for an unbounded number of concurrent operations, they propose no means of checking that these symmetry conditions hold on any given system. On the contrary, we show that verifying conflict serializability without bounding the number of concurrent operations is EXPSPACE-complete.…”