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Concurrent Data Structures Linked in Time
Arguments about correctness of a concurrent data structure are typically
carried out by using the notion of linearizability and specifying the
linearization points of the data structure's procedures. Such arguments are
often cumbersome as the linearization points' position in time can be dynamic
(depend on the interference, run-time values and events from the past, or even
future), non-local (appear in procedures other than the one considered), and
whose position in the execution trace may only be determined after the
considered procedure has already terminated.
In this paper we propose a new method, based on a separation-style logic, for
reasoning about concurrent objects with such linearization points. We embrace
the dynamic nature of linearization points, and encode it as part of the data
structure's auxiliary state, so that it can be dynamically modified in place by
auxiliary code, as needed when some appropriate run-time event occurs. We name
the idea linking-in-time, because it reduces temporal reasoning to spatial
reasoning. For example, modifying a temporal position of a linearization point
can be modeled similarly to a pointer update in separation logic. Furthermore,
the auxiliary state provides a convenient way to concisely express the
properties essential for reasoning about clients of such concurrent objects. We
illustrate the method by verifying (mechanically in Coq) an intricate optimal
snapshot algorithm due to Jayanti, as well as some clients
Bounded Concurrent Timestamp Systems Using Vector Clocks
Shared registers are basic objects used as communication mediums in
asynchronous concurrent computation. A concurrent timestamp system is a higher
typed communication object, and has been shown to be a powerful tool to solve
many concurrency control problems. It has turned out to be possible to
construct such higher typed objects from primitive lower typed ones. The next
step is to find efficient constructions. We propose a very efficient wait-free
construction of bounded concurrent timestamp systems from 1-writer multireader
registers. This finalizes, corrects, and extends, a preliminary bounded
multiwriter construction proposed by the second author in 1986. That work
partially initiated the current interest in wait-free concurrent objects, and
introduced a notion of discrete vector clocks in distributed algorithms.Comment: LaTeX source, 35 pages; To apper in: J. Assoc. Comp. Mac
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