Alan P. Sexton

KCM: A Knowledge Crunching Machine

KCM (Knowledge Crunching Machine) is a high-performance back-end processor which, coupled to a UNIX* desk-top workstation, provides a powerful and user-friendly Prolog environment catering for both development and execution of significant Prolog applications. This paper gives a general overview of the architecture of KCM stressing some new features like a 64-bit tagged architecture, shallow backtracking and an original memory management unit. Some early benchmark results obtained on prototype machines are presented. They show that KCM, which runs at a peak speed of 833 Klips on list concatenation, compares favorably with other dedicated Prolog machines and available commercial systems running on fast general purpose processors.

A Linear Grammar Approach to Mathematical Formula Recognition from PDF

Many approaches have been proposed over the years for the recognition of mathematical formulae from scanned documents. More recently a need has arisen to recognise formulae from PDF documents. Here we can avoid ambiguities introduced by traditional OCR approaches and instead extract perfect knowledge of the characters used in formulae directly from the document. This can be exploited by formula recognition techniques to achieve correct results and high performance. In this paper we revisit an old grammatical approach to formula recognition, that of Anderson from 1968, and assess its applicability with respect to data extracted from PDF documents. We identify some problems of the original method when applied to common mathematical expressions and show how they can be overcome. The simplicity of the original method leads to a very efficient recognition technique that not only is very simple to implement but also yields results of high accuracy for the recognition of mathematical formulae from PDF documents.

Abstract matrices in symbolic computation

We introduce a new data type of abstract matrices that allows the description of underspecified matrices containing ellipses and their use as templates for classes of concrete matrices. We present a series of algorithms that fully analyses the structure of abstract matrices and their representation and supports subsequent instantiation to concrete matrices.

Towards a parser for mathematical formula recognition

For the transfer of mathematical knowledge from paper to electronic form, the reliable automatic analysis and understanding of mathematical texts is crucial. A robust system for this task needs to combine low level character recognition with higher level structural analysis of mathematical formulas. We present progress towards this goal by extending a database-driven optical character recognition system for mathematics with two high level analysis features. One extends and enhances the traditional approach of projection profile cutting. The second aims at integrating the recognition process with graph grammar rewriting by giving support to the interactive construction and validation of grammar rules. Both approaches can be successfully employed to enhance the capabilities of our system to recognise and reconstruct compound mathematical expressions.

Bulk Loading the M-Tree to Enhance Query Performance

The M-tree is a paged, dynamically balanced metric access method that responds gracefully to the insertion of new objects. Like many spatial access methods, the M-tree’s performance is largely dependent on the degree of overlap between spatial regions represented by nodes in the tree, and minimisation of overlap is key to many of the design features of the M-tree and related structures. We present a novel approach to overlap minimisation using a new bulk loading algorithm, resulting in a query cost saving of between 25% and 40% for non-uniform data.

Chemical structure recognition: a rule-based approach

In chemical literature much information is given in the form of diagrams depicting molecules. In order to access this information diagrams have to be recognised and translated into a processable format. We present an approach that models the principal recognition steps for molecule diagrams in a strictly rule based system, providing rules to identify the main components - atoms and bonds - as well as to resolve possible ambiguities. The result of the process is a translation into a graph representation that can be used for further processing. We show the effectiveness of our approach by describing its embedding into a full recognition system and present an experimental evaluation that demonstrates how our current implementation outperforms the leading open source system currently available.

Processing textbook-style matrices

In mathematical textbooks matrices are often represented as objects of indefinite size containing abbreviations. To make the knowledge implicitly given in these representations available in electronic form they have to be interpreted correctly. We present an algorithm that provides the interface between the textbook style representation of matrix expressions and their concrete interpretation as formal mathematical objects. Given an underspecified matrix containing ellipses and fill symbols, our algorithm extracts the semantic information contained. Matrices are interpreted as a collection of regions that can be interpolated with a particular term structure. The effectiveness of our procedure is demonstrated with an implementation in the computer algebra system Maple.

Faithful mathematical formula recognition from PDF documents

We present an approach to extracting mathematical formulae directly from PDF documents. We exploit both the perfect character information as well as additional font and spacing information available from a PDF document to ensure a faithful recognition of mathematical expressions. The extracted information can be post-processed to produce suitable markup that can be re-inserted into the PDF documents in order to enable the handling of mathematical formulae by accessibility technology. Furthermore, we demonstrate how we recognise different types of mathematical objects, such as relations, operators, etc., without reference to predefined knowledge or dictionary lookup, using character clustering and interspace and character font information alone, all of which contributes to our goal of reconstructing the intended semantics of a formula from its presentation.

Reasoning about B+ Trees with Operational Semantics and Separation Logic

The B+ tree is an ordered tree structure with a fringe list. It is the most widely used data structure for data organisation and searching in database systems specifically, and, probably, computing in general. In this paper, we apply two techniques from programming language theory to B+ trees: operational semantics, in the form of an abstract machine, and separation logic. We use an abstract machine to give a precise and tractable formalisation of the operations on B+ trees. Separation logic is then used to formalise a data structure invariant for B+ trees and to establish correctness by showing that the invariant is preserved by the operations. As usual in separation logic, a frame property is essential for keeping the reasoning local. In our setting, that means that we concentrate on the subtree reached from the top of the stack of the abstract machine, while the remainder of the B+ tree stays invariant. A particularly attractive feature of this approach is the smooth way that proofs can cope with algorithms that begin with a tree descent and switch to fringe list traversal.

MaxTract: converting PDF to LATEX, MathML and text

In this paper we present the first public, online demonstration of MaxTract; a tool that converts PDF files containing mathematics into multiple formats including