@article{Graeter2020,
  author    = {Gr{\"a}ter, Joachim},
  title     = {Free division rings of fractions of crossed products of groups with Conradian left-orders},
  series = {Forum mathematicum},
  volume    = {32},
  journal   = {Forum mathematicum},
  number    = {3},
  publisher = {De Gruyter},
  address   = {Berlin},
  issn      = {0933-7741},
  doi       = {10.1515/forum-2019-0264},
  pages     = {739 -- 772},
  year      = {2020},
  abstract  = {Let D be a division ring of fractions of a crossed product F[G, eta, alpha], where F is a skew field and G is a group with Conradian left-order <=. For D we introduce the notion of freeness with respect to <= and show that D is free in this sense if and only if D can canonically be embedded into the endomorphism ring of the right F-vector space F((G)) of all formal power series in G over F with respect to <=. From this we obtain that all division rings of fractions of F[G, eta, alpha] which are free with respect to at least one Conradian left-order of G are isomorphic and that they are free with respect to any Conradian left-order of G. Moreover, F[G, eta, alpha] possesses a division ring of fraction which is free in this sense if and only if the rational closure of F[G, eta, alpha] in the endomorphism ring of the corresponding right F-vector space F((G)) is a skew field.},
  language  = {en}
}
@article{LorenzClemensSchroetteretal.2022,
  author    = {Lorenz, Claas and Clemens, Vera Elisabeth and Schr{\"o}tter, Max and Schnor, Bettina},
  title     = {Continuous verification of network security compliance},
  series = {IEEE transactions on network and service management},
  volume    = {19},
  journal   = {IEEE transactions on network and service management},
  number    = {2},
  publisher = {Institute of Electrical and Electronics Engineers},
  address   = {New York},
  issn      = {1932-4537},
  doi       = {10.1109/TNSM.2021.3130290},
  pages     = {1729 -- 1745},
  year      = {2022},
  abstract  = {Continuous verification of network security compliance is an accepted need. Especially, the analysis of stateful packet filters plays a central role for network security in practice. But the few existing tools which support the analysis of stateful packet filters are based on general applicable formal methods like Satifiability Modulo Theories (SMT) or theorem prover and show runtimes in the order of minutes to hours making them unsuitable for continuous compliance verification. In this work, we address these challenges and present the concept of state shell interweaving to transform a stateful firewall rule set into a stateless rule set. This allows us to reuse any fast domain specific engine from the field of data plane verification tools leveraging smart, very fast, and domain specialized data structures and algorithms including Header Space Analysis (HSA). First, we introduce the formal language FPL that enables a high-level human-understandable specification of the desired state of network security. Second, we demonstrate the instantiation of a compliance process using a verification framework that analyzes the configuration of complex networks and devices - including stateful firewalls - for compliance with FPL policies. Our evaluation results show the scalability of the presented approach for the well known Internet2 and Stanford benchmarks as well as for large firewall rule sets where it outscales state-of-the-art tools by a factor of over 41.},
  language  = {en}
}