Proceedings First Workshop on Logics and Model-checking for Self-* Systems

This volume contains the proceedings of the First Workshop on Logics and Model-checking for self-* systems (MOD* 2014). The worshop took place in Bertinoro, Italy, on 12th of September 2014, and was a satellite event of iFM 2014 (the 11th International Conference on Integrated Formal Methods). The workshop focuses on demonstrating the applicability of Formal Methods on modern complex systems with a high degree of self-adaptivity and reconfigurability, by bringing together researchers and practitioners with the goal of pushing forward the state of the art on logics and model checking.

Smooth solutions of the Euler and Navier-Stokes equations from the a posteriori analysis of approximate solutions

The main result of [C. Morosi and L. Pizzocchero, Nonlinear Analysis, 2012] is presented in a variant, based on a C^infinity formulation of the Cauchy problem; in this approach, the a posteriori analysis of an approximate solution gives a bound on the Sobolev distance of any order between the exact and the approximate solution.

Tracking and Characterizing Botnets Using Automatically Generated Domains

Modern botnets rely on domain-generation algorithms (DGAs) to build resilient command-and-control infrastructures. Recent works focus on recognizing automatically generated domains (AGDs) from DNS traffic, which potentially allows to identify previously unknown AGDs to hinder or disrupt botnets communication capabilities. The state-of-the-art approaches require to deploy low-level DNS sensors to access data whose collection poses practical and privacy issues, making their adoption problematic. We propose a mechanism that overcomes the above limitations by analyzing DNS traffic data through a combination of linguistic and IP-based features of suspicious domains. In this way, we are able to identify AGD names, characterize their DGAs and isolate logical groups of domains that represent the respective botnets. Moreover, our system enriches these groups with new, previously unknown AGD names, and produce novel knowledge about the evolving behavior of each tracked botnet. We used our system in real-world settings, to help researchers that requested intelligence on suspicious domains and were able to label them as belonging to the correct botnet automatically. Additionally, we ran an evaluation on 1,153,516 domains, including AGDs from both modern (e.g., Bamital) and traditional (e.g., Conficker, Torpig) botnets. Our approach correctly isolated families of AGDs that belonged to distinct DGAs, and set automatically generated from non-automatically generated domains apart in 94.8 percent of the cases.

On power series solutions for the Euler equation, and the Behr-Necas-Wu initial datum

We consider the Euler equation for an incompressible fluid on a three dimensional torus, and the construction of its solution as a power series in time. We point out some general facts on this subject, from convergence issues for the power series to the role of symmetries of the initial datum. We then turn the attention to a paper by Behr, Necas and Wu in ESAIM: M2AN 35 (2001) 229-238; here, the authors chose a very simple Fourier polynomial as an initial datum for the Euler equation and analyzed the power series in time for the solution, determining the first 35 terms by computer algebra. Their calculations suggested for the series a finite convergence radius tau_3 in the H^3 Sobolev space, with 0.32 < tau_3 < 0.35; they regarded this as an indication that the solution of the Euler equation blows up. We have repeated the calculations of Behr, Necas and Wu, using again computer algebra; the order has been increased from 35 to 52, using the symmetries of the initial datum to speed up computations. As for tau_3, our results agree with the original computations of Behr, Necas and Wu (yielding in fact to conjecture that 0.32 < tau_3 < 0.33). Moreover, our analysis supports the following conclusions: (a) The finiteness of tau_3 is not at all an indication of a possible blow-up. (b) There is a strong indication that the solution of the Euler equation does not blow up at a time close to tau_3. In fact, the solution is likely to exist, at least, up to a time theta_3 > 0.47. (c) Pade analysis gives a rather weak indication that the solution might blow up at a later time.

From Regular to Strictly Locally Testable Languages

A classical result (often credited to Y. Medvedev) states that every language recognized by a finite automaton is the homomorphic image of a local language, over a much larger so-called local alphabet, namely the alphabet of the edges of the transition graph. Local languages are characterized by the value k=2 of the sliding window width in the McNaughton and Paperts infinite hierarchy of strictly locally testable languages (k-slt). We generalize Medvedevs result in a new direction, studying the relationship between the width and the alphabetic ratio telling how much larger the local alphabet is. We prove that every regular language is the image of a k-slt language on an alphabet of doubled size, where the width logarithmically depends on the automaton size, and we exhibit regular languages for which any smaller alphabetic ratio is insufficient. More generally, we express the trade-off between alphabetic ratio and width as a mathematical relation derived from a careful encoding of the states. At last we mention some directions for theoretical development and application.

Casimir operators, abelian subspaces and u-cohomology

This survey paper is an exposition of old and recent results of Kostant and al. on the relationships between the exterior algebra of a simple Lie algebra and the action of the Casimir operator on it. Our exposition relies on u-cohomology and it is basically self-contained.