🍩 Database of Original & Non-Theoretical Uses of Topology

1. Topology in Cyber Research (2022)

   Steve Huntsman, Jimmy Palladino, Michael Robinson

   Abstract

   We give an idiosyncratic overview of applications of topology to cyber research, spanning the analysis of variables/assignments and control flow in computer programs, a brief sketch of topological data analysis in one dimension, and the use of sheaves to analyze wireless networks. The text is from a chapter in the forthcoming book Mathematics in Cyber Research, to be published by Taylor and Francis.

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   • Networks
   • Software engineering
   • Networks
   • computer programs
   • Dowker complex
   • Path homology
   • sheaves

2. Topological Differential Testing (2020)

   Kristopher Ambrose, Steve Huntsman, Michael Robinson, Matvey Yutin

   Abstract

   We introduce topological differential testing (TDT), an approach to extracting the consensus behavior of a set of programs on a corpus of inputs. TDT uses the topological notion of a simplicial complex (and implicitly draws on richer topological notions such as sheaves and persistence) to determine inputs that cause inconsistent behavior and in turn reveal \emph\de facto\ input specifications. We gently introduce TDT with a toy example before detailing its application to understanding the PDF file format from the behavior of various parsers. Finally, we discuss theoretical details and other possible applications.

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   • Binary classifier
   • Differential testing
   • Software engineering
   • Dowker complex
   • Persistence
   • Sheaf theory