Implementing Feferman-Landin Logic. The objective of this project is to utilise computer based verification tools (such as PVS and Rewritting Logic) to develop a software engineering environment for specifying and verifying systems written in high-level programming languages such as Java, Scheme, and ML. The project will thus subtantially advance the use of formal computer based tools to develop reliable programs and specifications for life-critical systems. The project will also develop form ....Implementing Feferman-Landin Logic. The objective of this project is to utilise computer based verification tools (such as PVS and Rewritting Logic) to develop a software engineering environment for specifying and verifying systems written in high-level programming languages such as Java, Scheme, and ML. The project will thus subtantially advance the use of formal computer based tools to develop reliable programs and specifications for life-critical systems. The project will also develop formally
based interoperability between the PVS and Maude systems, two widely
used computer tools for reasoning about complex systems.Read moreRead less
Mathematics of Elliptic Curve Cryptography. The Australian society and economy requires fast, reliable, and secure digital infrastructure. First-generation security solutions cannot support the efficiency and scalability requirements of wireless and embedded consumer applications. New security infrastructures are emerging and must be carefully, but rapidly, defined and analysed. Thus developing a new framework in this area is one of the most important and urgent tasks. Besides, the intended wor ....Mathematics of Elliptic Curve Cryptography. The Australian society and economy requires fast, reliable, and secure digital infrastructure. First-generation security solutions cannot support the efficiency and scalability requirements of wireless and embedded consumer applications. New security infrastructures are emerging and must be carefully, but rapidly, defined and analysed. Thus developing a new framework in this area is one of the most important and urgent tasks. Besides, the intended work advances our knowledge of the theory and the quality of our culture. As such, it will promote the Australian science and will also have many practical applications in Computer Security and E-Commerce.Read moreRead less
Algorithms and computation in four-dimensional topology. This project will establish Australia as a world leader in computational topology, particularly in the all-important areas of topology in three and four dimensions. In four dimensions this work will be truly groundbreaking; until now the field has seen little development due to the complexity of the algorithms and computations required, and the applicant is in the unique position of having the necessary tools to make significant progress ....Algorithms and computation in four-dimensional topology. This project will establish Australia as a world leader in computational topology, particularly in the all-important areas of topology in three and four dimensions. In four dimensions this work will be truly groundbreaking; until now the field has seen little development due to the complexity of the algorithms and computations required, and the applicant is in the unique position of having the necessary tools to make significant progress in a feasible time frame. In three dimensions this project will strengthen the distinguished computational topology community in Melbourne, led by pioneers such as Rubinstein, Goodman, Hodgson as well as the applicant himself.Read moreRead less
RichProlog, a System for Deducing, Inducing and Learning in the Declarative Programming Paradigm. The aim of the project is to contribute to bridge the gap between learning and logic, theoretically and practically. Our purpose is to extend considerably the scope of the declarative programming paradigm, and build a system that can be used to solve learning or discovery problems as encountered in Artificial Intelligence. The system will enable rapid prototyping when applied to problems involving d ....RichProlog, a System for Deducing, Inducing and Learning in the Declarative Programming Paradigm. The aim of the project is to contribute to bridge the gap between learning and logic, theoretically and practically. Our purpose is to extend considerably the scope of the declarative programming paradigm, and build a system that can be used to solve learning or discovery problems as encountered in Artificial Intelligence. The system will enable rapid prototyping when applied to problems involving deduction, induction, and nonmonotonic reasoning. We intend the system to become a standard tool for tackling a broad range of applications, and the underlying theory to provide new insights on the logical foundations of Artificial Intelligence.
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Exploring the Frontiers of Feasible Computation. The project aims to delineate the boundary between feasible and infeasible computational problems. A problem is considered feasible if there is an algorithm to solve it in worst-case time bounded by a polynomial in the input size. This is probably impossible for the important class of NP-complete problems. However, typical examples of NP-complete problems can often be solved in polynomial time, because worst-case problems are rare. The project is ....Exploring the Frontiers of Feasible Computation. The project aims to delineate the boundary between feasible and infeasible computational problems. A problem is considered feasible if there is an algorithm to solve it in worst-case time bounded by a polynomial in the input size. This is probably impossible for the important class of NP-complete problems. However, typical examples of NP-complete problems can often be solved in polynomial time, because worst-case problems are rare. The project is relevant to public-key cryptography, where breaking an encryption scheme should be infeasible, and to many real-life situations where NP-complete problems need to be solved, either exactly or approximately.Read moreRead less
Efficient Computational Methods for Constrained Path Problems. We consider a class of path design problems which arise when an object needs to traverse between two points through a specified region. The region may be a continuous space or the path may be restricted to the edges of a network. The path must optimise a prescribed criterion such
as risk, reliability or cost and satisfy a number of constraints.
Problems of this type readily arise in the defence, transport and
communication i ....Efficient Computational Methods for Constrained Path Problems. We consider a class of path design problems which arise when an object needs to traverse between two points through a specified region. The region may be a continuous space or the path may be restricted to the edges of a network. The path must optimise a prescribed criterion such
as risk, reliability or cost and satisfy a number of constraints.
Problems of this type readily arise in the defence, transport and
communication industries. In addition to efficient solution methods
for these problems the project will produce computational tools for
a wide range of related network routing problems.Read moreRead less
Mathematics of Cryptography. The Australian society and economy requires fast, reliable, and secure communication. First-generation security solutions are not capable of supporting the efficiency and scalability requirements of mass-market adoption of wireless and embedded consumer applications. New security infrastructures are emerging and must be carefully, but rapidly, defined. Thus developing new mathematically solid tools in this area is one of the most important and urgent tasks. Besides, ....Mathematics of Cryptography. The Australian society and economy requires fast, reliable, and secure communication. First-generation security solutions are not capable of supporting the efficiency and scalability requirements of mass-market adoption of wireless and embedded consumer applications. New security infrastructures are emerging and must be carefully, but rapidly, defined. Thus developing new mathematically solid tools in this area is one of the most important and urgent tasks. Besides, the intended work advances our knowledge of the theory and the quality of our culture. As such, it will promote the Australian science and will also have many practical applications in Cryptography, Computer Security and E-Commerce.Read moreRead less
Quantum correlations in ultra-cold Fermi gases. The field of ultra-cold Fermi gases provides a unique opportunity to develop and test theoretical methods for novel experimental environments of exceptional purity and simplicity. This improved understanding will have potential applications in many fields, ranging from the astrophysics of neutron stars to condensed matter systems such as superconductors or nanostructures. Just as importantly, the project will develop linkages with world leading the ....Quantum correlations in ultra-cold Fermi gases. The field of ultra-cold Fermi gases provides a unique opportunity to develop and test theoretical methods for novel experimental environments of exceptional purity and simplicity. This improved understanding will have potential applications in many fields, ranging from the astrophysics of neutron stars to condensed matter systems such as superconductors or nanostructures. Just as importantly, the project will develop linkages with world leading theoretical groups, which will greatly aid research student education. There are direct applications to experiments on molecule formation with ultra-cold fermions in the ARC Centre of Excellence for Quantum-Atom Optics.Read moreRead less
Coarse Grained Parallel Algorithms. Various fields of research face barriers created by problems that are computationally hard and/or require processing of large amounts of data. For example, some computational biochemistry methods on protein or gene sequences can not be scaled up to data sets required for human health research because of performance problems. Parallel computing enables new research by increasing the size of solvable problems. In addition to fundamental parallel computing resear ....Coarse Grained Parallel Algorithms. Various fields of research face barriers created by problems that are computationally hard and/or require processing of large amounts of data. For example, some computational biochemistry methods on protein or gene sequences can not be scaled up to data sets required for human health research because of performance problems. Parallel computing enables new research by increasing the size of solvable problems. In addition to fundamental parallel computing research, this project studies parallel algorithms for structure-based drug design and protein-protein interaction prediction that will enable new biochemistry research, as well as parallel algorithms for data cubes that will help enable the next generation of very large data warehouses.Read moreRead less
Unsupervised learning of finite mixture models in data mining applications. The extraction of useful information from massively large databases is known as data mining. Its broad but vague goal is to find "interesting structure" in the data, which typically leads to breaking the data into clusters. To this end, we consider the fast, efficient, and automatic learning of finite mixture models in hugh data sets without any prior knowledge of the structure. This probabilistic approach to the discove ....Unsupervised learning of finite mixture models in data mining applications. The extraction of useful information from massively large databases is known as data mining. Its broad but vague goal is to find "interesting structure" in the data, which typically leads to breaking the data into clusters. To this end, we consider the fast, efficient, and automatic learning of finite mixture models in hugh data sets without any prior knowledge of the structure. This probabilistic approach to the discovery and validation of group structure in data mining applications will considerably enhance knowledge management and decision support in science, industry, and government.
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