Mechanised foundations of proof calculi. Commercial program verification tools based upon special-purpose logic-based proof calculi can now guarantee that large programs are free of specific bugs. But who verifies the proof-calculi? Our research will lead to tools to automatically verify proof-calculi and will eventually help to avoid costly post-construction debugging.
Evidence-based frameworks for security protocol verification. Security protocols are an essential part of secure communication networks. This project aims to develop verification techniques for security protocols that produce independently verifiable formal certificates of correctness. The project's outcome will contribute to the certification processes for secure network systems at the highest level of assurance.
Mathematical, logical and computational foundations of hybrid control systems, and their application to design and synthesis problems in control engineering. Hybrid control systems are mathematical models of heterogeneous systems consisting of digital computer components interacting in real-time with continuous physical processes. Their many engineering applications include air traffic control, medical technology and automated transport. Motivated by such safety-critical and high-confidence appl ....Mathematical, logical and computational foundations of hybrid control systems, and their application to design and synthesis problems in control engineering. Hybrid control systems are mathematical models of heterogeneous systems consisting of digital computer components interacting in real-time with continuous physical processes. Their many engineering applications include air traffic control, medical technology and automated transport. Motivated by such safety-critical and high-confidence applications, the project aims to develop a unified framework of mathematical logics adequate to formally represent and reason about the structure, behaviour, and properties of hybrid control systems, and use this to develop methodologies for automatically synthesising hybrid control programs that are provably correct with respect to their specifications. Other outcomes include prototype software implementations of hybrid controller design tools.Read moreRead less
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
Multicast in Single-Hop and Multi-Hop WDM Optical Networks. The emerging Wavelength-Division-Multiplexing (WDM) optical network is a promising candidate for next-generation Internet, which provides enormous bandwidth and fast connectivity. Multicast in WDM networks is a fundamental problem which has wide applications including teleconferencing, entertainment distribution, etc. In this project we investigate the multicast and constraint multicast problems in both single-hop and multi-hop WDM netw ....Multicast in Single-Hop and Multi-Hop WDM Optical Networks. The emerging Wavelength-Division-Multiplexing (WDM) optical network is a promising candidate for next-generation Internet, which provides enormous bandwidth and fast connectivity. Multicast in WDM networks is a fundamental problem which has wide applications including teleconferencing, entertainment distribution, etc. In this project we investigate the multicast and constraint multicast problems in both single-hop and multi-hop WDM networks by studying their computational complexities and devising scalable, high-quality approximation algorithms for them. The developed algorithms significantly improve the network performance and scalability, and the innovative approaches and algorithm techniques developed in this project are also applicable to other routing problems.Read moreRead less
Practical and theoretical aspects of structure enumeration. Many areas of study involve processing of large numbers of
objects in some class. These are countless examples in
chemistry, physics, mathematics, and other disciplines.
Structure Enumeration is the study of methods for efficient
generation and analysis of such objects. The project will
involve exploitation and extension of recent advances, many
due to the CI, which have added orders of magnitude to what
was possible only a few ....Practical and theoretical aspects of structure enumeration. Many areas of study involve processing of large numbers of
objects in some class. These are countless examples in
chemistry, physics, mathematics, and other disciplines.
Structure Enumeration is the study of methods for efficient
generation and analysis of such objects. The project will
involve exploitation and extension of recent advances, many
due to the CI, which have added orders of magnitude to what
was possible only a few years ago. The outcome will be a
combination of theoretical results and practical achievements,
whose usefulness will be demonstrated with some serious
applications in physics and mathematics.
Read moreRead less
Structure enumeration, applications and analysis. Structure enumeration and analysis is at the heart of finite mathematics and its many fields of application in diverse scientific disciplines. Australia has a substantial status in this field both in mathematics and physics. This project will enhance that status and develop greater ties with the centres of structure research in other parts of the world.
Proof Theoretical Methods for Reasoning about Process Equivalence. The emergence of internet commerce has made the issue of secure computing more urgent than ever. A substantial part of the security issues with today's computer applications are due to design problems.
The principles of secure computation have not been fully understood and adequate tools for the construction of secure applications are still lacking. The understanding of the foundations of secure computation is essential in bu ....Proof Theoretical Methods for Reasoning about Process Equivalence. The emergence of internet commerce has made the issue of secure computing more urgent than ever. A substantial part of the security issues with today's computer applications are due to design problems.
The principles of secure computation have not been fully understood and adequate tools for the construction of secure applications are still lacking. The understanding of the foundations of secure computation is essential in building trusted computer applications. Process calculi and logic represent two promising disciplines in which the principles of analysis and design of secure systems can be studied systematically, out of which formal verification tools can be constructed.Read moreRead less
Expressive power and complexity of temporal logics for model-checking. Hardware verification based upon mathematical logic is now routinely
used in industry to verify the correctness of large digital circuits
using a technique called model-checking. Such discrete systems move
from one state to another according to the regular ticks of a clock.
The challenge now is to find tractable methods for reasoning about
real-time systems and hybrid systems that move in a continuous manner
with respec ....Expressive power and complexity of temporal logics for model-checking. Hardware verification based upon mathematical logic is now routinely
used in industry to verify the correctness of large digital circuits
using a technique called model-checking. Such discrete systems move
from one state to another according to the regular ticks of a clock.
The challenge now is to find tractable methods for reasoning about
real-time systems and hybrid systems that move in a continuous manner
with respect to time: examples include aeroplanes flying according to
the laws of physics and a moving robot arm. We shall invent new logics
which are specifically tailored for tractable reasoning about
real-time and hybrid systems.Read moreRead less
Machine-checked Foundations for Verified Vote Counting. The project will deliver a general methodology for developing formal logical specifications of the Acts of Parliament for many common systems for counting votes in preferential elections. The project will deliver corresponding computer programs to count votes according to these systems and will deliver formal independently checkable proofs that the programs meet their specification. Such formally verified computer programs provide a legally ....Machine-checked Foundations for Verified Vote Counting. The project will deliver a general methodology for developing formal logical specifications of the Acts of Parliament for many common systems for counting votes in preferential elections. The project will deliver corresponding computer programs to count votes according to these systems and will deliver formal independently checkable proofs that the programs meet their specification. Such formally verified computer programs provide a legally sound basis for counting votes by computer. The methodology will also allow electoral commissioners to improve the natural language descriptions of the relevant Acts of Parliament which are often woefully out of date with current practice.Read moreRead less