Effective Invariant Theory of Permutation Groups using Representation Theory

Using the theory of representations of the symmetric group, we propose an algorithm to compute the invariant ring of a permutation group. Our approach have the goal to reduce the amount of linear algebra computations and exploit a thinner combinatorial description of the invariant ring.Comment: Draft version, the corrected full version is available at http://www.springer.com

A combinatorial approach to knot recognition

This is a report on our ongoing research on a combinatorial approach to knot recognition, using coloring of knots by certain algebraic objects called quandles. The aim of the paper is to summarize the mathematical theory of knot coloring in a compact, accessible manner, and to show how to use it for computational purposes. In particular, we address how to determine colorability of a knot, and propose to use SAT solving to search for colorings. The computational complexity of the problem, both in theory and in our implementation, is discussed. In the last part, we explain how coloring can be utilized in knot recognition

JWalk: a tool for lazy, systematic testing of java classes by design introspection and user interaction

Popular software testing tools, such as JUnit, allow frequent retesting of modified code; yet the manually created test scripts are often seriously incomplete. A unit-testing tool called JWalk has therefore been developed to address the need for systematic unit testing within the context of agile methods. The tool operates directly on the compiled code for Java classes and uses a new lazy method for inducing the changing design of a class on the fly. This is achieved partly through introspection, using Java’s reflection capability, and partly through interaction with the user, constructing and saving test oracles on the fly. Predictive rules reduce the number of oracle values that must be confirmed by the tester. Without human intervention, JWalk performs bounded exhaustive exploration of the class’s method protocols and may be directed to explore the space of algebraic constructions, or the intended design state-space of the tested class. With some human interaction, JWalk performs up to the equivalent of fully automated state-based testing, from a specification that was acquired incrementally

Portunes: analyzing multi-domain insider threats

The insider threat is an important problem in securing information systems. Skilful insiders use attack vectors that yield the greatest chance of success, and thus do not limit themselves to a restricted set of attacks. They may use access rights to the facility where the system of interest resides, as well as existing relationships with employees. To secure a system, security professionals should therefore consider attacks that include non-digital aspects such as key sharing or exploiting trust relationships among employees. In this paper, we present Portunes, a framework for security design and audit, which incorporates three security domains: (1) the security of the computer system itself (the digital domain), (2) the security of the location where the system is deployed (the physical domain) and (3) the security awareness of the employees that use the system (the social domain). The framework consists of a model, a formal language and a logic. It allows security professionals to formally model elements from the three domains in a single framework, and to analyze possible attack scenarios. The logic enables formal specification of the attack scenarios in terms of state and transition properties