Data-flow Analysis of Programs with Associative Arrays

Dynamic programming languages, such as PHP, JavaScript, and Python, provide built-in data structures including associative arrays and objects with similar semantics-object properties can be created at run-time and accessed via arbitrary expressions. While a high level of security and safety of applications written in these languages can be of a particular importance (consider a web application storing sensitive data and providing its functionality worldwide), dynamic data structures pose significant challenges for data-flow analysis making traditional static verification methods both unsound and imprecise. In this paper, we propose a sound and precise approach for value and points-to analysis of programs with associative arrays-like data structures, upon which data-flow analyses can be built. We implemented our approach in a web-application domain-in an analyzer of PHP code.Comment: In Proceedings ESSS 2014, arXiv:1405.055

Black hole encircled by a thin disk: fully relativistic solution

We give a full metric describing the gravitational field of a static and axisymmetric thin disk without radial pressure encircling a Schwarzschild black hole. The disk density profiles are astrophysically realistic, stretching from the horizon to radial infinity, yet falling off quickly at both these locations. The metric functions are expressed as finite series of Legendre polynomials. Main advantages of the solution are that (i) the disks have no edges, so their fields are everywhere regular (outside the horizon), and that (ii) all non-trivial metric functions are provided analytically and in closed forms. We examine and illustrate basic properties of the black-hole -- disk space-times.Comment: 14 page

Relativistic disks by Appell-ring convolutions

We present a new method for generating the gravitational field of thin disks within the Weyl class of static and axially symmetric spacetimes. Such a gravitational field is described by two metric functions: one satisfies the Laplace equation and represents the gravitational potential, while the other is determined by line integration. We show how to obtain analytic thin-disk solutions by convolving a certain weight function -- an Abel transformation of the physical surface-density profile -- with the Appell-ring potential. We thus re-derive several known thin-disk solutions while, in some cases, completing the metric by explicitly computing the second metric function. Additionally, we obtain the total gravitational field of several superpositions of a disk with the Schwarzschild black hole. While the superposition problem is simple (linear) for the potential, it is mostly not such for the second metric function. However, in particular cases, both metric functions of the superposition can be found explicitly. Finally, we discuss a simpler procedure which yields the potentials of power-law-density disks we studied recently.Comment: 20 pages, 4 figures, supplemental material is provided in the ancillary Mathematica notebook "holeyMorganMorganDisks.nb" and the MX file "holeyMorganMorganDisks.mx