Distribution-based bisimulation for labelled Markov processes

In this paper we propose a (sub)distribution-based bisimulation for labelled Markov processes and compare it with earlier definitions of state and event bisimulation, which both only compare states. In contrast to those state-based bisimulations, our distribution bisimulation is weaker, but corresponds more closely to linear properties. We construct a logic and a metric to describe our distribution bisimulation and discuss linearity, continuity and compositional properties.Comment: Accepted by FORMATS 201

Multiwavelength Observations of the Hot DB Star PG 0112+104

We present a comprehensive multiwavelength analysis of the hot DB white dwarf PG 0112+104. Our analysis relies on newly-acquired FUSE observations, on medium-resolution FOS and GHRS data, on archival high-resolution GHRS observations, on optical spectrophotometry both in the blue and around Halpha, as well as on time-resolved photometry. From the optical data, we derive a self-consistent effective temperature of 31,300+-500 K, a surface gravity of log g = 7.8 +- 0.1 (M=0.52 Msun), and a hydrogen abundance of log N(H)/N(He) < -4.0. The FUSE spectra reveal the presence of CII and CIII lines that complement the previous detection of CII transitions with the GHRS. The improved carbon abundance in this hot object is log N(C)/N(He) = -6.15 +- 0.23. No photospheric features associated with other heavy elements are detected. We reconsider the role of PG 0112+104 in the definition of the blue edge of the V777 Her instability strip in light of our high-speed photometry, and contrast our results with those of previous observations carried out at the McDonald Observatory.Comment: 10 pages in emulateapj, 9 figures, accepted for publication in Ap

Approximating a Behavioural Pseudometric without Discount for<br> Probabilistic Systems

Desharnais, Gupta, Jagadeesan and Panangaden introduced a family of behavioural pseudometrics for probabilistic transition systems. These pseudometrics are a quantitative analogue of probabilistic bisimilarity. Distance zero captures probabilistic bisimilarity. Each pseudometric has a discount factor, a real number in the interval (0, 1]. The smaller the discount factor, the more the future is discounted. If the discount factor is one, then the future is not discounted at all. Desharnais et al. showed that the behavioural distances can be calculated up to any desired degree of accuracy if the discount factor is smaller than one. In this paper, we show that the distances can also be approximated if the future is not discounted. A key ingredient of our algorithm is Tarski's decision procedure for the first order theory over real closed fields. By exploiting the Kantorovich-Rubinstein duality theorem we can restrict to the existential fragment for which more efficient decision procedures exist

Quantifying Timing Leaks and Cost Optimisation

We develop a new notion of security against timing attacks where the attacker is able to simultaneously observe the execution time of a program and the probability of the values of low variables. We then show how to measure the security of a program with respect to this notion via a computable estimate of the timing leakage and use this estimate for cost optimisation.Comment: 16 pages, 2 figures, 4 tables. A shorter version is included in the proceedings of ICICS'08 - 10th International Conference on Information and Communications Security, 20-22 October, 2008 Birmingham, U

Domain and Antidomain Semigroups

Abstract. We axiomatise and study operations for relational domain and antidomain on semigroups and monoids. We relate this approach with previous axiomatisations for semirings, partial transformation semi-groups and dynamic predicate logic.

Approximating Markov Processes by Averaging

We recast the theory of labelled Markov processes in a new setting, in a way "dual" to the usual point of view. Instead of considering state transitions as a collection of subprobability distributions on the state space, we view them as transformers of real-valued functions. By generalizing the operation of conditional expectation, we build a category consisting of labelled Markov processes viewed as a collection of operators; the arrows of this category behave as projections on a smaller state space. We define a notion of equivalence for such processes, called bisimulation, which is closely linked to the usual definition for probabilistic processes. We show that we can categorically construct the smallest bisimilar process, and that this smallest object is linked to a well-known modal logic. We also expose an approximation scheme based on this logic, where the state space of the approximants is finite; furthermore, we show that these finite approximants categorically converge to the smallest bisimilar process.Nous reconsidérons les processus de Markov étiquetés sous une nouvelle approche, dans un certain sens "dual'' au point de vue usuel. Au lieu de considérer les transitions d'état en état en tant qu'une collection de distributions de sous-probabilités sur l'espace d'états, nous les regardons en tant que transformations de fonctions réelles. En généralisant l'opération d'espérance conditionelle, nous construisons une catégorie où les objets sont des processus de Markov étiquetés regardés en tant qu'un rassemblement d'opérateurs; les flèches de cette catégorie se comportent comme des projections sur un espace d'états plus petit. Nous définissons une notion d'équivalence pour de tels processus, que l'on appelle bisimulation, qui est intimement liée avec la définition usuelle pour les processus probabilistes. Nous démontrons que nous pouvons construire, d'une manière catégorique, le plus petit processus bisimilaire à un processus donné, et que ce plus petit object est lié à une logique modale bien connue. Nous développons une méthode d'approximation basée sur cette logique, où l'espace d'états des processus approximatifs est fini; de plus, nous démontrons que ces processus approximatifs convergent, d'une manière catégorique, au plus petit processus bisimilaire

Simulation-Based Graph Similarity

We present symmetric and asymmetric similarity measures for labeled directed rooted graphs that are inspired by the simulation and bisimulation relations on labeled transition systems. Computation of the similarity measures has close connections to discounted Markov decision processes in the asymmetric case and to perfect-information stochastic games in the symmetric case. For the symmetric case, we also give a polynomial-time algorithm that approximates the similarity to any desired precision

A Comprehensive Spectroscopic Analysis of DB White Dwarfs

We present a detailed analysis of 108 helium-line (DB) white dwarfs based on model atmosphere fits to high signal-to-noise optical spectroscopy. We derive a mean mass of 0.67 Mo for our sample, with a dispersion of only 0.09 Mo. White dwarfs also showing hydrogen lines, the DBA stars, comprise 44% of our sample, and their mass distribution appears similar to that of DB stars. As in our previous investigation, we find no evidence for the existence of low-mass (M < 0.5 Mo) DB white dwarfs. We derive a luminosity function based on a subset of DB white dwarfs identified in the Palomar-Green survey. We show that 20% of all white dwarfs in the temperature range of interest are DB stars, although the fraction drops to half this value above Teff ~ 20,000 K. We also show that the persistence of DB stars with no hydrogen features at low temperatures is difficult to reconcile with a scenario involving accretion from the interstellar medium, often invoked to account for the observed hydrogen abundances in DBA stars. We present evidence for the existence of two different evolutionary channels that produce DB white dwarfs: the standard model where DA stars are transformed into DB stars through the convective dilution of a thin hydrogen layer, and a second channel where DB stars retain a helium-atmosphere throughout their evolution. We finally demonstrate that the instability strip of pulsating V777 Her white dwarfs contains no nonvariables, if the hydrogen content of these stars is properly accounted for.Comment: 74 pages including 30 figures, accepted for publication in the Astrophysical Journa

Comparative branching-time semantics for Markov chains

This paper presents various semantics in the branching-time spectrum of discrete-time and continuous-time Markov chains (DTMCs and CTMCs).\ud Strong and weak bisimulation equivalence and simulation pre-orders are covered and are logically characterised in terms of the temporal logics PCTL (Probabilistic Computation Tree Logic) and CSL (Continuous Stochastic Logic). Apart from presenting various existing branching-time relations in a uniform manner, this paper presents the following new results: (i) strong simulation for CTMCs, (ii) weak simulation for CTMCs and DTMCs, (iii) logical characterizations thereof (including weak bisimulation for DTMCs), (iv) a relation between weak bisimulation and weak simulation equivalence, and (v) various connections between equivalences and pre-orders in the continuous- and discrete-time setting. The results are summarized in a branching-time spectrum for DTMCs and CTMCs elucidating their semantics as well as their relationship