We introduce abortable and query-abortable object types intended for implementation in asynchronous shared-memory systems with low contention. Implementations of such types behave like ordinary objects when accessed sequentially, but may abort operations when accessed concurrently. An aborted operation may or may not take effect, i.e., cause a state transition, and it returns no indication of which possibility occurred. Since this uncertainty can be problematic, a query-abortable type supports a QUERY operation that each process can use to determine its last non-QUERY operation on the object that caused a state transition, and the response associated with this state transition. Our research is closely related to obstruction-free implementations (introduced by Herlihy, Luchangco and Moir) and responsive obstruction-free implementations (introduced by Attiya, Guerraoui and Kouznetsov). Like abortable and query-abortable types, these implementations may exhibit degraded behaviour in the face of contention. We show that abortable registers--registers strictly weaker than safe registers--can be used to obtain obstruction-free and responsive obstruction-free implementations for any type. We present universal constructions for abortable and query-abortable types that are novel and efficient in the number of registers used. Specifically, they are based on a simple timestamping mechanism for detecting concurrent executions, and, in systems with n processes, use only n abortable registers or only O(n^2) single-reader, single-writer abortable registers. The timestamping mechanism we introduce is based on the inc&read counter type and appears to be interesting in its own right. As a generalization, we study the k-inc&read counter types, for k>0. We also identify a potential problem with correctness properties based on step contention: with such properties, the composition of correct object implementations may result in an implementation that is not correct. In other words, implementations defined in terms of step contention are not always composable. To avoid this problem, we introduce a property based on interval contention, namely non-triviality, to define the correct behaviour of abortable and query-abortable object implementations.

We introduce abortable and query-abortable object types intended for implementation in asynchronous shared-memory systems with low contention. Implementations of such types behave like ordinary objects when accessed sequentially, but may abort operations when accessed concurrently. An aborted operation may or may not take effect, i.e., cause a state transition, and it returns no indication of which possibility occurred. Since this uncertainty can be problematic, a query-abortable type supports a QUERY operation that each process can use to determine its last non-QUERY operation on the object that caused a state transition, and the response associated with this state transition. Our research is closely related to obstruction-free implementations (introduced by Herlihy, Luchangco and Moir) and responsive obstruction-free implementations (introduced by Attiya, Guerraoui and Kouznetsov). Like abortable and query-abortable types, these implementations may exhibit degraded behaviour in the face of contention. We show that abortable registers--registers strictly weaker than safe registers--can be used to obtain obstruction-free and responsive obstruction-free implementations for any type. We present universal constructions for abortable and query-abortable types that are novel and efficient in the number of registers used. Specifically, they are based on a simple timestamping mechanism for detecting concurrent executions, and, in systems with n processes, use only n abortable registers or only O(n^2) single-reader, single-writer abortable registers. The timestamping mechanism we introduce is based on the inc&read counter type and appears to be interesting in its own right. As a generalization, we study the k-inc&read counter types, for k>0. We also identify a potential problem with correctness properties based on step contention: with such properties, the composition of correct object implementations may result in an implementation that is not correct. In other words, implementations defined in terms of step contention are not always composable. To avoid this problem, we introduce a property based on interval contention, namely non-triviality, to define the correct behaviour of abortable and query-abortable object implementations.