Concurrent Timestamping Made Simple

Concurrent Time-stamp Systems (ctss) allow processes to temporally order concurrent events in an asynchronous shared memory system, a powerful tool for concurrency control, serving as the basis for solutions to coordination problems such as mutual exclusion, `-exclusion, randomized consensus, and multi-writer multi-reader atomic registers. Solutions to these problems all use an \unbounded number" based concurrent time-stamp system (uctss), a construction which is as simple to use as it is to understand. A bounded \black-box" replacement of uctss would imply equally simple bounded solutions to most of these extensively researched problems. Unfortunately, while all know applications use uctss, all existing solution algorithms are only proven to implement the Dolev-Shavit ctss axioms, which have been widely criticized as \hard-to-use." While it is easy to show that a uctss implements the ctss axioms, there is no proof that a system meeting the ctss axioms implements uctss. Thus, the problem of constructing a bounded black-box replacement for uctss remains open. This paper presents the rst such bounded black-box replacement of uctss. The key to the solution is a simpliied variant of the Dolev-Shavit ctss algorithm based on the atomic snapshot object proposed by Afek et. al. and Anderson, in a way that limits the number of interleavings that can occur, and whose behaviours can be readily mapped to those of uctss. Using the forward simulation techniques of the I/O Automata model, we are then able show that our bounded algorithm behaves like uctss. The forward simulation allows us to present, what would otherwise be a complicated proof, as an extensive, yet at each step simple case analysis. In fact, we believe that large parts of the forward simulation proof can be checked using an automatic proof checker such as Larch. For read/write memory, our easy to use bounded uctss is only a logaritmic factor from the most eecient known bounded ctss constructions. Moreover, unlike these eecient algorithms, our modular use of an atomic snapshot object implies that our constructions are not limited to read/write memory, and can be applied in any computation model whose basic operations suuce to provide a wait-free snapshot implementation. The complexity of our bounded uctss will be the same as the complexity of the underlaying snapshot implementation used.