Probabilistic Opacity in Refinement-Based Modeling

Given a probabilistic transition system (PTS) $\cal A$ partially observed by an attacker, and an $\omega$-regular predicate $\varphi$over the traces of $\cal A$, measuring the disclosure of the secret $\varphi$ in $\cal A$ means computing the probability that an attacker who observes a run of $\cal A$ can ascertain that its trace belongs to $\varphi$. In the context of refinement, we consider specifications given as Interval-valued Discrete Time Markov Chains (IDTMCs), which are underspecified Markov chains where probabilities on edges are only required to belong to intervals. Scheduling an IDTMC $\cal S$ produces a concrete implementation as a PTS and we define the worst case disclosure of secret $\varphi$ in ${\cal S}$ as the maximal disclosure of $\varphi$ over all PTSs thus produced. We compute this value for a subclass of IDTMCs and we prove that refinement can only improve the opacity of implementations

Revisiting bisimilarity and its modal logic for nondeterministic and probabilistic processes

We consider PML, the probabilistic version of Hennessy-Milner logic introduced by Larsen and Skou to characterize bisimilarity over probabilistic processes without internal nondeterminism.We provide two different interpretations for PML by considering nondeterministic and probabilistic processes as models, and we exhibit two new bisimulation-based equivalences that are in full agreement with those interpretations. Our new equivalences include as coarsest congruences the two bisimilarities for nondeterministic and probabilistic processes proposed by Segala and Lynch. The latter equivalences are instead in agreement with two versions of Hennessy-Milner logic extended with an additional probabilistic operator interpreted over state distributions rather than over individual states. Thus, our new interpretations of PML and the corresponding new bisimilarities offer a uniform framework for reasoning on processes that are purely nondeterministic or reactive probabilistic or are mixing nondeterminism and probability in an alternating/non-alternating way

Nature and number of distinct phases in the random field Ising model

We investigate the phase structure of the random-field Ising model with a bimodal random field distribution. Our aim is to test for the possibility of an equilibrium spin-glass phase, and for replica symmetry breaking (RSB) within such a phase. We study a low-temperature region where the spin-glass phase is thought to occur, but which has received little numerical study to date. We use the exchange Monte-Carlo technique to acquire equilibrium information about the model, in particular the $P(q)$ distribution and the spectrum of eigenvalues of the spin-spin correlation matrix (which tests for the presence of RSB). Our studies span the range in parameter space from the ferromagnetic to the paramagnetic phase. We find however no convincing evidence for any equilibrium glass phase, with or without RSB, between these two phases. Instead we find clear evidence (principally from the $P(q)$ distribution) that there are only two phases at this low temperature, with a discontinuity in the magnetization at the transition like that seen at other temperatures.Comment: 10 pages, 8 figures, submitted to PRB, original submission had fig4 and fig5 not readable. No changes have been mad