Abstract. An alternating projection of a prime link can to used to produce a group presentation (of the link group under free product with the infinite cyclic group) with some useful peculiarities, including small cancellation conditions. In this presentation, conjugacy diagrams are shown to have the form of a tiling of squares in the Euclidean plane in one of a limited number of shapes. An argument based on the shape of the link projection is used to show that the tiling requires no more square tiles than a linear function of word length (with constant multiple based on the number of link crossings). It follows that the computation time for testing conjugacy of two group elements (previously known to be no worse than exponential) is bounded by a cubic polynomial. This bounds complexity in the original link group.
Gersten and Short showed that group presentations satisfying certain minimal small cancellation conditions are automatic. The automatic structure they described does not have unique group element representatives. It is easy, however, to modify their language to produce an automatic spanning tree of geodesics: that is, an automatic structure of geodesics which is both prefix-closed and has unique representatives. When combined with a construction showing that all geodesic representatives of a group element are encoded in a tiling of a particular geometric form, this shows that in fact the language of lexicographically least geodesics is also automatic (it is clearly a spanning tree).
This paper describes an approach for improving cyber resilience through the synthesis of optimal microsegmentation policy for a network. By leveraging microsegmentation security architecture, we can reason about fine-grained policy rules that enforce access for given combinations of source address, destination address, destination port, and protocol. Our approach determines microsegmentation policy rules that limit adversarial movement within a network according to assumed attack scenarios and mission availability needs. For this problem, we formulate a novel optimization objective function that balances cyberattack risks against accessibility to critical network resources. Given the application of a particular set of policy rules as a candidate optimal solution, this objective function estimates the adversary effort for carrying out a particular attack scenario, which it balances against the extent to which the solution restricts access to mission-critical services. We then apply artificial intelligence techniques (evolutionary programming) to learn microsegmentation policy rules that optimize this objective function.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.