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We investigate the power of randomness in two-party communication complexity. In particular, we study the model where the parties can make a constant number of queries to a function with an efficient one-sided-error randomized protocol. The complexity classes defined by this model comprise the Randomized Boolean Hierarchy, which is analogous to the Boolean Hierarchy but defined with one-sided-error randomness instead of nondeterminism. Our techniques connect the Nondeterministic and Randomized Boolean Hierarchies, and we provide a complete picture of the relationships among complexity classes within and across these two hierarchies. In particular, we prove that the Randomized Boolean Hierarchy does not collapse, and we prove a query-to-communication lifting theorem for all levels of the Nondeterministic Boolean Hierarchy and use it to resolve an open problem stated in the paper by Halstenberg and Reischuk (CCC 1988) which initiated the study of this hierarchy.
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A Survey of Graph Comparison Methods with Applications to Nondeterminism in High-Performance Computing
The convergence of extremely high levels of hardware concurrency and the effective overlap of computation and communication in asynchronous executions has resulted in increasing nondeterminism in High-Performance Computing (HPC) applications. Nondeterminism can manifest at multiple levels: from low-level communication primitives to libraries to application-level functions. No matter its source, nondeterminism can drastically increase the cost of result reproducibility, debugging workflows, testing parallel programs, or ensuring fault-tolerance. Nondeterministic executions of HPC applications can be modeled as event graphs, and the applications’ nondeterministic behavior can be understood and, in some cases, mitigated using graph comparison algorithms. However, a connection between graph comparison algorithms and approaches to understanding nondeterminism in HPC still needs to be established. This survey article moves the first steps toward establishing a connection between graph comparison algorithms and nondeterminism in HPC with its three contributions: it provides a survey of different graph comparison algorithms and a timeline for each category’s significant works; it discusses how existing graph comparison methods do not fully support properties needed to understand nondeterministic patterns in HPC applications; and it presents the open challenges that should be addressed to leverage the power of graph comparisons for the study of nondeterminism in HPC applications.
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- Award ID(s):
- 1900888
- PAR ID:
- 10432143
- Editor(s):
- Sage
- Date Published:
- Journal Name:
- The International Journal of High Performance Computing Applications
- ISSN:
- 1094-3420
- Page Range / eLocation ID:
- 109434202311666
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1177/10943420231166610
