Towards a topological characterization of asynchronous complexity
PODC '97 Proceedings of the sixteenth annual ACM symposium on Principles of distributed computing
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Concurrent Timestamp Systems (CTSS) allow processes to temporally order concurrent events in an asynchronous shared memory system. Bounded memory constructions of a CTSS are extremely powerful tools for concurrency control, and are the basis for solutions to many coordination problems including mutual exclusion, randomized consensus, and multiwriter multireader atomic registers. Unfortunately, known bounded CTSS constructions seem to be complex from the algorithmic point of view. Because of the importance of bounded , CTSS the rather involved original construction by Dolev and Shavit was followed by a series of papers that tried to provide more easily verifiable CTSS constructions. In this paper, we present what we believe is the simplest, most modular, and most easily proven bounded CTSS algorithm known to date. The algorithm is constructed and its correctness proven by carefully reasoned use of several tools. Our algorithm combines the labeling method of the Dolev-Shavit CTSS with the atomic snapshot algorithm proposed in Afek et. al, in a way that limits the number of interleavings that can occur. To facilitate our correctness proof, we introduce a specially tailored intermediate CTSS specification using unbounded label values taken from the positive reals. Our correctness proof first shows that the real-number based specification meets the CTSS axioms. Using the forward simulation techniques of the I/O Automata model, we then show that our bounded algorithm implements the real-number based specification. Finally, we prove that any CTSS that meets the CTSS axioms can be used to implement multireader multiwriter atomic registers and first-some-first-serve (fcfs) mutual exclusion.