Identifying Product Order with Restricted Boltzmann Machines

Unsupervised machine learning via a restricted Boltzmann machine is an useful tool in distinguishing an ordered phase from a disordered phase. Here we study its application on the two-dimensional Ashkin-Teller model, which features a partially ordered product phase. We train the neural network with spin configuration data generated by Monte Carlo simulations and show that distinct features of the product phase can be learned from non-ergodic samples resulting from symmetry breaking. Careful analysis of the weight matrices inspires us to define a nontrivial machine-learning motivated quantity of the product form, which resembles the conventional product order parameter.Comment: 9 pages, 11 figure

A Program Logic for Verifying Secure Routing Protocols

The Internet, as it stands today, is highly vulnerable to attacks. However, little has been done to understand and verify the formal security guarantees of proposed secure inter-domain routing protocols, such as Secure BGP (S-BGP). In this paper, we develop a sound program logic for SANDLog-a declarative specification language for secure routing protocols for verifying properties of these protocols. We prove invariant properties of SANDLog programs that run in an adversarial environment. As a step towards automated verification, we implement a verification condition generator (VCGen) to automatically extract proof obligations. VCGen is integrated into a compiler for SANDLog that can generate executable protocol implementations; and thus, both verification and empirical evaluation of secure routing protocols can be carried out in this unified framework. To validate our framework, we encoded several proposed secure routing mechanisms in SANDLog, verified variants of path authenticity properties by manually discharging the generated verification conditions in Coq, and generated executable code based on SANDLog specification and ran the code in simulation