On the Computational Power of Shared Objects

Abstract. We propose a new classification for evaluating the strength of shared objects. The classification is based on finding, for each object of type o, the strongest progress condition for which it is possible to solve consensus for any number of processes, using any number of objects of type o and atomic registers. We use the strongest progress condition to associate with each object a number call the power number of that object. Objects with higher power numbers are considered stronger. Then, we define the power hierarchy which is an infinite hi-erarchy of objects such that the objects at level i of the hierarchy are exactly those objects with power number i. Comparing our classification with the traditional one which is based on fixing the progress condition (namely, wait-freedom) and finding the largest number of processes for which consensus is solvable, reveals interesting results. Our equivalence and extended universality results, provide a deeper understanding of the nature of the relative computational power of shared objects

The Computational Structure of Progress Conditions

Abstract. Understanding the effect of different progress conditions on the com-putability of distributed systems is an important and exciting research direction. For a system with n processes, we define exponentially many new progress con-ditions and explore their properties and strength. We cover all the known, sym-metric and asymmetric, progress conditions and many new interesting conditions. Together with our technical results, the new definitions provide a deeper under-standing of synchronization and concurrency

Foreword: Parallelism in Algorithms and Architectures

This special issue contains 6 selected papers whose preliminary versions appeared in the Proceedings of the 23rd Annual ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), held June 2011, in San Jose, California, USA. These papers were selected by the special issue co-editors from 35 papers that were presented at the conference. The authors were invited to submit full versions of their papers, which were then fully refereed according to the usual standards of Theory of Computing Systems. The selected papers are representative of the breadth and depth of the research in parallelism in algorithms and architectures that was presented at SPAA 2011

Computer-Assisted Verification of an Algorithm for Concurrent Timestamps

A formal representation and machine-checked proof are given for the Bounded Concurrent Timestamp (BCTS) algorithm of Dolev and Shavit. The proof uses invariant assertions and a forward simulation mapping to a corresponding Unbounded Concurrent Timestamp (UCTS) algorithm, following a strategy developed by Gawlick, Lynch, and Shavit. The proof was produced interactively, using the Larch Prover. Keywords Verification, validation and testing; tools and tool support; Larch; input/output automata; concurrent timestamps 1 INTRODUCTION In this paper, we describe a computer-assisted verification, using the Larch Prover (Garland and Guttag, 1991), of one of the most complicated algorithms in the distributed systems theory literature: the Bounded Concurrent Timestamp (BCTS) algorithm of Dolev and Shavit (1989). This algorithm runs in the single-writer, multi-reader, read/write shared memory model. The verified algorithm is a slight simplification, due to Gawlick, Lynch, and Shavit (1992), of t..