Modal Interface Automata

De Alfaro and Henzinger's Interface Automata (IA) and Nyman et al.'s recent combination IOMTS of IA and Larsen's Modal Transition Systems (MTS) are established frameworks for specifying interfaces of system components. However, neither IA nor IOMTS consider conjunction that is needed in practice when a component shall satisfy multiple interfaces, while Larsen's MTS-conjunction is not closed and Bene\v{s} et al.'s conjunction on disjunctive MTS does not treat internal transitions. In addition, IOMTS-parallel composition exhibits a compositionality defect. This article defines conjunction (and also disjunction) on IA and disjunctive MTS and proves the operators to be 'correct', i.e., the greatest lower bounds (least upper bounds) wrt. IA- and resp. MTS-refinement. As its main contribution, a novel interface theory called Modal Interface Automata (MIA) is introduced: MIA is a rich subset of IOMTS featuring explicit output-must-transitions while input-transitions are always allowed implicitly, is equipped with compositional parallel, conjunction and disjunction operators, and allows a simpler embedding of IA than Nyman's. Thus, it fixes the shortcomings of related work, without restricting designers to deterministic interfaces as Raclet et al.'s modal interface theory does.Comment: 28 page

Young and intermediate-age massive star clusters

An overview of our current understanding of the formation and evolution of star clusters is given, with main emphasis on high-mass clusters. Clusters form deeply embedded within dense clouds of molecular gas. Left-over gas is cleared within a few million years and, depending on the efficiency of star formation, the clusters may disperse almost immediately or remain gravitationally bound. Current evidence suggests that a few percent of star formation occurs in clusters that remain bound, although it is not yet clear if this fraction is truly universal. Internal two-body relaxation and external shocks will lead to further, gradual dissolution on timescales of up to a few hundred million years for low-mass open clusters in the Milky Way, while the most massive clusters (> 10^5 Msun) have lifetimes comparable to or exceeding the age of the Universe. The low-mass end of the initial cluster mass function is well approximated by a power-law distribution, dN/dM ~ M^{-2}, but there is mounting evidence that quiescent spiral discs form relatively few clusters with masses M > 2 x 10^5 Msun. In starburst galaxies and old globular cluster systems, this limit appears to be higher, at least several x 10^6 Msun. The difference is likely related to the higher gas densities and pressures in starburst galaxies, which allow denser, more massive giant molecular clouds to form. Low-mass clusters may thus trace star formation quite universally, while the more long-lived, massive clusters appear to form preferentially in the context of violent star formation.Comment: 21 pages, 3 figures. To appear as invited review article in a special issue of the Phil. Trans. Royal Soc. A: Ch. 9 "Star clusters as tracers of galactic star-formation histories" (ed. R. de Grijs). Fully peer reviewed. PDFLaTeX, requires rspublic.cls style fil

On Zone-Based Analysis of Duration Probabilistic Automata

We propose an extension of the zone-based algorithmics for analyzing timed automata to handle systems where timing uncertainty is considered as probabilistic rather than set-theoretic. We study duration probabilistic automata (DPA), expressing multiple parallel processes admitting memoryfull continuously-distributed durations. For this model we develop an extension of the zone-based forward reachability algorithm whose successor operator is a density transformer, thus providing a solution to verification and performance evaluation problems concerning acyclic DPA (or the bounded-horizon behavior of cyclic DPA).Comment: In Proceedings INFINITY 2010, arXiv:1010.611

Exact String Solutions in Nontrivial Backgrounds

We show how the classical string dynamics in $D$-dimensional gravity background can be reduced to the dynamics of a massless particle constrained on a certain surface whenever there exists at least one Killing vector for the background metric. We obtain a number of sufficient conditions, which ensure the existence of exact solutions to the equations of motion and constraints. These results are extended to include the Kalb-Ramond background. The $D1$-brane dynamics is also analyzed and exact solutions are found. Finally, we illustrate our considerations with several examples in different dimensions. All this also applies to the tensionless strings.Comment: 22 pages, LaTeX, no figures; V2:Comments and references added; V3:Discussion on the properties of the obtained solutions extended, a reference and acknowledgment added; V4:The references renumbered, to appear in Phys Rev.

Constraining star cluster disruption mechanisms

Star clusters are found in all sorts of environments and their formation and evolution is inextricably linked to the star formation process. Their eventual destruction can result from a number of factors at different times, but the process can be investigated as a whole through the study of the cluster age distribution. Observations of populous cluster samples reveal a distribution following a power law of index approximately -1. In this work we use M33 as a test case to examine the age distribution of an archetypal cluster population and show that it is in fact the evolving shape of the mass detection limit that defines this trend. That is to say, any magnitude-limited sample will appear to follow a dN/dt=1/t, while cutting the sample according to mass gives rise to a composite structure, perhaps implying a dependence of the cluster disruption process on mass. In the context of this framework, we examine different models of cluster disruption from both theoretical and observational standpoints.Comment: To appear in the proceedings of IAU Symposium 266: "Star Clusters: Basic Galactic Building Blocks Throughout Time And Space", eds. R. de Grijs and J. Lepin

Compositional Safety Logics

In this paper we present a generalisation of a promising compositional model-checking technique introduced for finite-state systems by Andersen in [And95] and extended to networks of timedautomata by Larsen et al in [LPY95a, LL95, LPY95b, KLL+97a].In our generalized setting, programs are modelled as arbitrary(possibly infinite-state) transition systems and verified with respectto properties of a basic safety logic. As the fundamentalprerequisite of the compositional technique, it is shown how logicalproperties of a parallel program may be transformed intonecessary and sufficient properties of components of the program.Finally, a set of axiomatic laws are provided useful forsimplifying formulae and complete with respect to validity andunsatisfiability

Hennessy-Milner Logic with Greatest Fixed Points as a Complete Behavioural Specification Theory

There are two fundamentally different approaches to specifying and verifying properties of systems. The logical approach makes use of specifications given as formulae of temporal or modal logics and relies on efficient model checking algorithms; the behavioural approach exploits various equivalence or refinement checking methods, provided the specifications are given in the same formalism as implementations. In this paper we provide translations between the logical formalism of Hennessy-Milner logic with greatest fixed points and the behavioural formalism of disjunctive modal transition systems. We also introduce a new operation of quotient for the above equivalent formalisms, which is adjoint to structural composition and allows synthesis of missing specifications from partial implementations. This is a substantial generalisation of the quotient for deterministic modal transition systems defined in earlier papers

Circular String-Instabilities in Curved Spacetime

We investigate the connection between curved spacetime and the emergence of string-instabilities, following the approach developed by Loust\'{o} and S\'{a}nchez for de Sitter and black hole spacetimes. We analyse the linearised equations determining the comoving physical (transverse) perturbations on circular strings embedded in Schwarzschild, Reissner-Nordstr\"{o}m and de Sitter backgrounds. In all 3 cases we find that the "radial" perturbations grow infinitely for $r\rightarrow 0$ (ring-collapse), while the "angular" perturbations are bounded in this limit. For $r\rightarrow\infty$ we find that the perturbations in both physical directions (perpendicular to the string world-sheet in 4 dimensions) blow up in the case of de Sitter space. This confirms results recently obtained by Loust\'{o} and S\'{a}nchez who considered perturbations around the string center of mass.Comment: 24 pages Latex + 2 figures (not included). Observatoire de Paris, Meudon No. 9305

Stable and Unstable Circular Strings in Inflationary Universes

It was shown by Garriga and Vilenkin that the circular shape of nucleated cosmic strings, of zero loop-energy in de Sitter space, is stable in the sense that the ratio of the mean fluctuation amplitude to the loop radius is constant. This result can be generalized to all expanding strings (of non-zero loop-energy) in de Sitter space. In other curved spacetimes the situation, however, may be different. In this paper we develop a general formalism treating fluctuations around circular strings embedded in arbitrary spatially flat FRW spacetimes. As examples we consider Minkowski space, de Sitter space and power law expanding universes. In the special case of power law inflation we find that in certain cases the fluctuations grow much slower that the radius of the underlying unperturbed circular string. The inflation of the universe thus tends to wash out the fluctuations and to stabilize these strings.Comment: 15 pages Latex, NORDITA 94/14-