Strong Equivalence Relations for Iterated Models
Abstract
The Iterated Immediate Snapshot model (IIS), due to its elegant geometrical representation, has become standard for applying topological reasoning to distributed computing. Its modular structure makes it easier to analyze than the more realistic (noniterated) readwrite AtomicSnapshot memory model (AS). It is known that AS and IIS are equivalent with respect to \emph{waitfree task} computability: a distributed task is solvable in AS if and only if it solvable in IIS. We observe, however, that this equivalence is not sufficient in order to explore solvability of tasks in \emph{submodels} of AS (i.e. proper subsets of its runs) or computability of \emph{longlived} objects, and a stronger equivalence relation is needed. In this paper, we consider \emph{adversarial} submodels of AS and IIS specified by the sets of processes that can be \emph{correct} in a model run. We show that AS and IIS are equivalent in a strong way: a (possibly longlived) object is implementable in AS under a given adversary if and only if it is implementable in IIS under the same adversary. %This holds whether the object is oneshot or longlived. Therefore, the computability of any object in shared memory under an adversarial AS scheduler can be equivalently investigated in IIS.
 Publication:

arXiv eprints
 Pub Date:
 February 2014
 arXiv:
 arXiv:1402.2446
 Bibcode:
 2014arXiv1402.2446B
 Keywords:

 Computer Science  Distributed;
 Parallel;
 and Cluster Computing;
 Computer Science  Data Structures and Algorithms;
 C.2.4;
 F.1.1