Kleene algebra with domain

We propose Kleene algebra with domain (KAD), an extension of Kleene algebra with two equational axioms for a domain and a codomain operation, respectively. KAD considerably augments the expressiveness of Kleene algebra, in particular for the specification and analysis of state transition systems. We develop the basic calculus, discuss some related theories and present the most important models of KAD. We demonstrate applicability by two examples: First, an algebraic reconstruction of Noethericity and well-foundedness; second, an algebraic reconstruction of propositional Hoare logic.Comment: 40 page

Two Extrasolar Asteroids with Low Volatile-Element Mass Fractions

Using ultraviolet spectra obtained with the Cosmic Origins Spectrograph on the Hubble Space Telescope, we extend our previous ground-based optical determinations of the composition of the extrasolar asteroids accreted onto two white dwarfs, GD 40 and G241-6. Combining optical and ultraviolet spectra of these stars with He-dominated atmospheres, 13 and 12 polluting elements are confidently detected in GD 40 and G241-6, respectively. For the material accreted onto GD 40, the volatile elements C and S are deficient by more than a factor of 10 and N by at least a factor of 5 compared to their mass fractions in primitive CI chondrites and approach what is inferred for bulk Earth. A similar pattern is found for G241-6 except that S is undepleted. We have also newly detected or placed meaningful upper limits for the amount of Cl, Al, P, Ni and Cu in the accreted matter. Extending results from optical studies, the mass fractions of refractory elements in the accreted parent bodies are similar to what is measured for bulk Earth and chondrites. Thermal processing, perhaps interior to a snow line, appears to be of central importance in determining the elemental compositions of these particular extrasolar asteroids.Comment: 37 pages, 13 figures, 5 tables, ApJ, accepte

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

Ancient planetary systems are orbiting a large fraction of white dwarf stars

Infrared studies have revealed debris likely related to planet formation in orbit around ~30% of youthful, intermediate mass, main sequence stars. We present evidence, based on atmospheric pollution by various elements heavier than helium, that a comparable fraction of the white dwarf descendants of such main sequence stars are orbited by planetary systems. These systems have survived, at least in part, through all stages of stellar evolution that precede the white dwarf. During the time interval (~200 million years) that a typical polluted white dwarf in our sample has been cooling it has accreted from its planetary system the mass of one of the largest asteroids in our solar system (e.g., Vesta or Ceres). Usually, this accreted mass will be only a fraction of the total mass of rocky material that orbits these white dwarfs; for plausible planetary system configurations we estimate that this total mass is likely to be at least equal to that of the Sun's asteroid belt, and perhaps much larger. We report abundances of a suite of 8 elements detected in the little studied star G241-6 that we find to be among the most heavily polluted of all moderately bright white dwarfs.Comment: 31 pages, 4 figures, 5 tables. Accepted for the Astrophysical

Infrared Signatures of Disrupted Minor Planets at White Dwarfs

Spitzer Space Observatory IRAC and MIPS photometric observations are presented for 20 white dwarfs with T < 20,000 K and metal-contaminated photospheres. A warm circumstellar disk is detected at GD 16 and likely at PG 1457-086, while the remaining targets fail to reveal mid-infrared excess typical of dust disks, including a number of heavily polluted stars. Extending previous studies, over 50% of all single white dwarfs with implied metal accretion rates dM/dt > 3e8 g/s display a warm infrared excess from orbiting dust; the likely result of a tidally-destroyed minor planet. This benchmark accretion rate lies between the dust production rates of 1e6 g/s in the solar system zodiacal cloud and 1e10 g/s often inferred for debris disks at main sequence A-type stars. It is estimated that between 1% and 3% of all single white dwarfs with cooling ages less than around 0.5 Gyr possess circumstellar dust, signifying an underlying population of minor planets.Comment: 47 pages, accepted to Ap

Characterising Probabilistic Processes Logically

In this paper we work on (bi)simulation semantics of processes that exhibit both nondeterministic and probabilistic behaviour. We propose a probabilistic extension of the modal mu-calculus and show how to derive characteristic formulae for various simulation-like preorders over finite-state processes without divergence. In addition, we show that even without the fixpoint operators this probabilistic mu-calculus can be used to characterise these behavioural relations in the sense that two states are equivalent if and only if they satisfy the same set of formulae.Comment: 18 page

The theta-join as a join with theta

We present an algebra for the classical database operators. Contrary to most approaches we use (inner) join and projection as the basic operators. Theta joins result by representing theta as a database table itself and defining theta-join as a join with that table. The same technique works for selection. With this, (point-free) proofs of the standard optimisation laws become very simple and uniform. The approach also applies to proving join/projection laws for preference queries. Extending the earlier approach of [16], we replace disjointness assumptions on the table types by suitable consistency conditions. Selected results have been machine-verified using the CALCCHECK tool

Testing Reactive Probabilistic Processes

We define a testing equivalence in the spirit of De Nicola and Hennessy for reactive probabilistic processes, i.e. for processes where the internal nondeterminism is due to random behaviour. We characterize the testing equivalence in terms of ready-traces. From the characterization it follows that the equivalence is insensitive to the exact moment in time in which an internal probabilistic choice occurs, which is inherent from the original testing equivalence of De Nicola and Hennessy. We also show decidability of the testing equivalence for finite systems for which the complete model may not be known

Compositionality for Quantitative Specifications

We provide a framework for compositional and iterative design and verification of systems with quantitative information, such as rewards, time or energy. It is based on disjunctive modal transition systems where we allow actions to bear various types of quantitative information. Throughout the design process the actions can be further refined and the information made more precise. We show how to compute the results of standard operations on the systems, including the quotient (residual), which has not been previously considered for quantitative non-deterministic systems. Our quantitative framework has close connections to the modal nu-calculus and is compositional with respect to general notions of distances between systems and the standard operations

Lumpability Abstractions of Rule-based Systems

The induction of a signaling pathway is characterized by transient complex formation and mutual posttranslational modification of proteins. To faithfully capture this combinatorial process in a mathematical model is an important challenge in systems biology. Exploiting the limited context on which most binding and modification events are conditioned, attempts have been made to reduce the combinatorial complexity by quotienting the reachable set of molecular species, into species aggregates while preserving the deterministic semantics of the thermodynamic limit. Recently we proposed a quotienting that also preserves the stochastic semantics and that is complete in the sense that the semantics of individual species can be recovered from the aggregate semantics. In this paper we prove that this quotienting yields a sufficient condition for weak lumpability and that it gives rise to a backward Markov bisimulation between the original and aggregated transition system. We illustrate the framework on a case study of the EGF/insulin receptor crosstalk.Comment: In Proceedings MeCBIC 2010, arXiv:1011.005