Symmetry in Software Synthesis

Abstract

With the surge of multi- and manycores, much research has focused on algorithms for mapping and scheduling on these complex platforms. Large classes of these algorithms face scalability problems. This is why diverse methods are commonly used for reducing the search space. While most such approaches leverage the inherent symmetry of architectures and applications, they do it in a problem-specific and intuitive way. However, intuitive approaches become impractical with growing hardware complexity, like Network-on-Chip interconnect or heterogeneous cores. In this paper, we present a formal framework that can determine the inherent symmetry of architectures and applications algorithmically and leverage these for problems in software synthesis. Our approach is based on the mathematical theory of groups and a generalization called inverse semigroups. We evaluate our approach in two state-of-the-art mapping frameworks. Even for the platforms with a handful of cores of today and moderate-size benchmarks, our approach consistently yields reductions of the overall execution time of algorithms, accelerating them by a factor up to 10 in our experiments, or improving the quality of the results.Comment: 31 pages, 18 figure

Generative Design of the Architecture Platform in Multiprocessor System Design

“…Eliminating redundant solutions, and thus reducing the size of the feasible solution space is therefore essential for the DSE of real-world use cases. In that context, Goens et al [39] identify redundant solutions for the task mapping problem on a grid-based architecture. They provide a framework for automatically identifying local and global symmetries using the concept of inverse semigroups.…”

Embeddings of Task Mappings to Multicore Systems

“…dim ← 2dim return ι execution time. This seems very plausible if we consider the symmetries of the problem [14], where multiple mappings are equivalent yet distinct. There are also other similarities in mappings.…”

Energy-efficient Runtime Resource Management for Adaptable Multi-application Mapping

“…Approaches such as [3], [17]- [19] use heuristics for efficient exploration of Pareto-optimal configurations, while others such as [4], [20] use evolutionary algorithms. The amount of considered configuration can be also reduced by exploiting system symmetries [21], [22].…”

“…To track the remaining progress rate of the job while iterating the mapping segments, the algorithm initialize ρ * in line 4 and updates it in lines 11 and 16. If the job is not finished after the last mapping segment, the new mapping segment is created and added to the schedule (lines[19][20][21][22].…”