A concurrent object is a data object shared by concurrent processes. Linearizability is a correctness condition for concurrent objects that exploits the semantics of abstract data types. It permits a high degree of concurrency, yet it permits programmers to specify and reason about concurrent objects using known techniques from the sequential domain. Linearizability provides the illusion that each operation applied by concurrent processes takes effect instantaneously at some point between its invocation and its response, implying that the meaning of a concurrent object’s operations can be given by pre- and post-conditions. This paper defines linearizability, compares it to other correctness conditions, presents and demonstrates a method for proving the correctness of implementations, and shows how to reason about concurrent objects, given they are linearizable.

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The inductive assertion method is generalized to permit formal, machine-verifiable proofs of correctness for multiprocess programs. Individual processes are represented by ordinary flowcharts, and no special synchronization mechanisms are assumed, so the method can be applied to a large class of multiprocess programs. A correctness proof can be designed together with the program by a hierarchical process of stepwise refinement, making the method practical for larger programs. The resulting proofs tend to be natural formalizations of the informal proofs that are now used.

A new solution to the mutual exclusion problem is presented that, in the absence of contention, requires only seven memory accesses. It assumes atomic reads and atomic writes to shared registers. Capsule Review To build a useful computing system from a collection of processors that communicate by sharing memory, but lack any atomic operation more complex than a memory read or write, it is necessary to implement mutual exclusion using only these operations. Solutions to this problem have been known for twenty years, but they are linear in the number of processors. Lamport presents a new algorithm which takes constant time (five writes and two reads) in the absence of contention, which is the normal case. To achieve this performance it sacrifices fairness, which is probably unimportant in practical applications. The paper gives an informal argument that the algorithm's performance in the absence of contention is optimal, and a fairly formal proof of safety and freedom from deadlock, u...

. This paper introduces a general formulation of atomic snapshot memory, a shared memory partitioned into words written (updated) by individual processes, or instantaneously read (scanned) in its entirety. This paper presents three wait-free implementations of atomic snapshot memory. The first implementation in this paper uses unbounded (integer) fields in these registers, and is particularly easy to understand. The second implementation uses bounded registers. Its correctness proof follows the ideas of the unbounded implementation. Both constructions implement a single-writer snapshot memory, in which each word may be updated by only one process, from single-writer, n-reader registers. The third algorithm implements a multi-writer snapshot memory from atomic n-writer, n-reader registers, again echoing key ideas from the earlier constructions. All operations require \Theta(n 2 ) reads and writes to the component shared registers in the worst case. Categories and Subject Discriptors:...

We investigate proof rules for information hiding, using the recent formalism of separation logic. In essence, we use the separating conjunction to partition the internal resources of a module from those accessed by the module's clients. The use of a logical connective gives rise to a form of dynamic partitioning, where we track the transfer of ownership of portions of heap storage between program components. It also enables us to enforce separation in the presence of mutable data structures with embedded addresses that may be aliased.

We develop a logic for reasoning about object-oriented programs. The logic is for a language with an imperative semantics and aliasing, and accounts for self-reference in objects. It is much like a type system for objects with subtyping, but our specifications go further than types in detailing pre- and postconditions. We intend the logic as an analogue of Hoare logic for objectoriented programs. Our main technical result is a soundness theorem that relates the logic to a standard operational semantics.

In this paper we show how a resource-oriented logic, separation logic, can be used to reason about the usage of resources in concurrent programs.

In the transition axiom method, safety properties of a concurrent system can be specified by programs; liveness properties are specified by assertions in a simple temporal logic. The method is described with some simple examples, and its logical foundation is informally explored through a careful examination of what it means to implement a specification. Language issues and other practical details are largely ignored.