Topological Differential Testing

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 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.