- Interacting Frobenius Algebras and the Structure of Multipartite Entanglement. Bob Coecke, Aleks Kissinger. Research report PRG-RR-09-12. pdf
- Abstract. Providing a generic description of entanglement in n-qubit systems is a long-standing open problem in quantum information science. A structural scheme for representing arbitrary multipartite entangled states will yield a deeper understanding of how they behave and interact as computational components within more general computational schemes and protocols. Here we provide such a description…
- Exploring a Quantum Theory with Graph Rewriting and Computer Algebra. Aleks Kissinger. In proceedings of Calculemus 2009. Spinger, 2009. pdf | springerlink
- Abstract. Graphical languages provide a powerful tool for describing the behaviour of quantum systems. While the use of graphs vastly reduces the complexity of many calculations, manual graphical manipulation quickly becomes untenable for large graphs or large numbers of graphs. To combat this issue, we are developing a tool called Quantomatic, which allows automated and semi-automated explorations of graph rewrite systems and their underlying semantics. We emphasise in this paper the features of Quantomatic that interact with a computer algebra system to discover graphical relationships via the unification of matrix equations. Since these equations can grow exponentially with the size of the graph, we use this method to discover small identities and use those identities as graph rewrites to expand the theory.
- Graph Rewrite Systems for Classical Structures in †-Symmetric Monoidal Categories. Masters thesis, 2008. pdf
- Abstract. This paper introduces several related graph rewrite systems derived from known identities on classical structures within a †-symmetric monoidal category. First, we develop a rewrite system based on a single classical structure, and use it to develop a proof of the so-called “spider-theorem,” where a connected graph containing a single classical structure can be uniquely determined by the number of inputs and outputs (i.e. it can be rewritten as a graph resembling an n-legged spider). These spiders are shown to be the normal forms of graphs containing a single classical structure. Next, complementary classical structures are introduced, as well as a new rewrite system on graphs of red and green spiders. A proof of convergence is given for a limited two-colour rewrite system, as well as insights into ways to approach normalisation in a more powerful rewrite system.
- Graph Rewriting for Classical Structures. Ross Duncan, Lucas Dixon, Aleks Kissinger. Poster presented at QICS 2008. pdf
- Intro. Complementary classical structures correspond concretely to copy and delete operations over a pair of mutually unbiased bases. When acting as the generators of a †-symmetric monoidal category, they provide a powerful computational primitive, with a simple graphical representation. We have shown that the induced graph rewrite system is well-behaved and lends itself to automation.
- Lopol: A Deductive Database Approach to Policy Analysis and Rewriting. Aleks Kissinger, John C. Hale. In proceedings of the Second Annual SELinux Symposium, 2006. pdf | slides
- Abstract. This paper presents a method for deductive database-driven analysis of Security-Enhanced Linux policies. First, it discusses how directives in an SELinux policy can be normalized and encoded as logical relations. Next, the paper describes how to use these relations in conjunction with inference rules to perform a number of simple analyses. The techniques used to detect security characteristics within a policy can then be applied to automated policy rewriting, where those characteristics (i.e. security goals) are actually projected onto the policy to generate a new one. The paper closes by discussing the use of a logical ruleset as a high-level language, allowing a policy writer to quickly tailor a large default policy (such as strict, targeted, or refpolicy) to the specific needs of a system or a class of systems.
