Model checking copy phases of concurrent copying garbage collection with various memory models

Abstract

Modern concurrent copying garbage collection (GC), in particular, real-time GC, uses fine-grained synchronizations with a mutator, which is the application program that mutates memory, when it moves objects in its copy phase. It resolves a data race using a concurrent copying protocol, which is implemented as interactions between the collector threads and the read and write barriers that the mutator threads execute. The behavioral effects of the concurrent copying protocol rely on the memory model of the CPUs and the programming languages in which the GC is implemented. It is difficult, however, to formally investigate the behavioral properties of concurrent copying protocols against various memory models. To address this problem, we studied the feasibility of the bounded model checking of concurrent copying protocols with memory models. We investigated a correctness-related behavioral property of copying protocols of various concurrent copying GC algorithms, including real-time GC Stopless, Clover, Chicken, Staccato, and Schism against six memory models, total store ordering (TSO), partial store ordering (PSO), relaxed memory ordering (RMO), and their variants, in addition to sequential consistency (SC) using bounded model checking. For each combination of a protocol and memory model, we conducted model checking with a model of a mutator. In this wide range of case studies, we found faults in two GC algorithms, one of which is relevant to the memory model. We fixed these faults with the great help of counterexamples. We also modified some protocols so that they work under some memory models weaker than those for which the original protocols were designed, and checked them using model checking. We believe that bounded model checking is a feasible approach to investigate behavioral properties of concurrent copying protocols under weak memory models.