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Classification results in quasigroup and loop theory via a combination of automated reasoning tools

Volker SorgeSimon ColtonRoy McCaslandAndreas Meier — 2008

Commentationes Mathematicae Universitatis Carolinae

We present some novel classification results in quasigroup and loop theory. For quasigroups up to size 5 and loops up to size 7, we describe a unique property which determines the isomorphism (and in the case of loops, the isotopism) class for any example. These invariant properties were generated using a variety of automated techniques --- including machine learning and computer algebra --- which we present here. Moreover, each result has been automatically verified, again using a variety of techniques...

Designing a Semantic Ground Truth for Mathematical Formulae

Sexton, AlanSorge, VolkerSuzuki, Masakazu — 2010

Towards a Digital Mathematics Library. Paris, France, July 7-8th, 2010

We report on a new project to design a semantic ground truth set for mathematical document analysis. The ground truth set will be generated by annotating recognised mathematical symbols with respect to both their global meaning in the context of the considered documents and their local function within the particular mathematical formula they occur. The aim of our work is to have a reliable database available for semantic classification during the formula recognition process with the aim of enabling...

Extracting Precise Data on the Mathematical Content of PDF Documents

Baker, Josef B.Sexton, Alan P.Sorge, Volker — 2008

Towards Digital Mathematics Library. Birmingham, United Kingdom, July 27th, 2008

As more and more scientific documents become available in PDF format, their automatic analysis becomes increasingly important. We present a procedure that extracts mathematical symbols from PDF documents by examining both the original PDF file and a rasterized version. This provides more precise information than is available either directly from the PDF file or by traditional character recognition techniques. The data can then be used to improve mathematical parsing methods that transform the mathematics...

An Online Repository of Mathematical Samples

Baker, Josef B.Sexton, Alan P.Sorge, Volker — 2009

Towards a Digital Mathematics Library. Grand Bend, Ontario, Canada, July 8-9th, 2009

With a growing community of researchers working on the recognition, parsing and digital exploitation of mathematical formulae, a need has arisen for a set of samples or benchmarks which can be used to compare, evaluate and help to develop different implementations and algorithms. The benchmark set would have to cover a wide range of mathematics, contain enough information to be able to search for specific samples and be accessible to the whole community. In this paper, we propose an on-line system...

Towards Reverse Engineering of PDF Documents

Baker, Josef B.Sexton, Alan P.Sorge, Volker — 2011

Towards a Digital Mathematics Library. Bertinoro, Italy, July 20-21st, 2011

We present a progress report on our ongoing project of reverse engineering scientific PDF documents. The aim is to obtain mathematical markup that can be used as source for regenerating a document that resembles the original as closely as possible. This source can then be a basis for further document processing. Our current tool uses specialised PDF extraction together with image analysis to produce near perfect input for parsing mathematical formula. Applying a linear grammar and specific drivers...

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