Symbolic execution and the testing of COBOL programs

The thesis is in two parts. Part one is a review of existing work in the area of software testing and more specifically symbolic execution. Part two is a description of the symbolic execution testing system for COBOL (SYM-BOL). Much of the work presented has been published or accepted for publication. Part one commences by introducing the aims of software testing and is followed by a review of the tools and techniques of software testing that have been developed over the past 25 years. A simple taxonomy of software testing techniques is given. One potentially powerful technique is symbolic execution. The principles of symbolic execution are described followed by the problems in applying symbolic execution. Part one is completed by a review of existing symbolic execution testing systems. No symbolic execution testing system has previously been built for a commercial data processing language such as COBOL. Part two commences by outlining the features of the SYM-BOL system and describes the user strategies that may be employed when using the system. The system generates an intermediate form in stages by transforming the source program into one that contains only a limited number of language constructs. Path selection can be automatic or undertaken by the user. In both cases the results of the symbolic execution already undertaken are available to the path selector to help reduce the likelihood of selecting an infeasible path. A description of how the Nag-library linear optimizer E04MBF is used for feasibility checking is given. Feasible solutions are turned into files of test cases. Simple assertions may be included in the source program which do not affect the normal execution of the software but which can be verified by inclusion in the symbolic execution

The detection efficiency of on-axis short gamma ray burst optical afterglows triggered by aLIGO/Virgo

Assuming neutron star (NS) or neutron star/stellar-mass black hole (BH) mergers as progenitors of the short gamma ray bursts, we derive and demonstrate a simple analysis tool for modelling the efficiency of recovering on-axis optical afterglows triggered by a candidate gravitational wave event detected by the Advanced LIGO and Virgo network. The coincident detection efficiency has been evaluated for different classes of operating telescopes using observations of gamma ray bursts. We show how the efficiency depends on the luminosity distribution of the optical afterglows, the telescope features, and the sky localisation of gravitational wave triggers. We estimate a plausible optical afterglow and gravitational wave coincidence rate of 1 yr$^{-1}$ (0.1 yr$^{-1}$) for NS-NS (NS-BH), and how this rate is scaled down in detection efficiency by the time it takes to image the gravitational wave sky localization and the limiting magnitude of the telescopes. For NS-NS (NS-BH) we find maximum detection efficiencies of $>80$ when the total imaging time is less than 200 min (80 min) and the limiting magnitude fainter than 20 (21). We show that relatively small telescopes $(m<18)$ can achieve similar detection efficiencies to meter class facilities $(m<20)$ with similar fields of view, only if the less sensitive instruments can respond to the trigger and image the field within 10-15 min. The inclusion of LIGO India into the gravitational wave observatory network will significantly reduce imaging time for telescopes with limiting magnitudes $\sim20$ but with modest fields of view. An optimal coincidence search requires a global network of sensitive and fast response wide field instruments that could effectively image relatively large gravitational-wave sky localisations and produce transient candidates for further photometric and spectroscopic follow-up.Comment: 6 pages, 2 figures, version 2, reference added typo correction, Accepted by MNRA

Nuclear Equation of State from Observations of Short Gamma-Ray Burst Remnants

The favoured progenitor model for short $\gamma$-ray bursts (SGRBs) is the merger of two neutron stars that triggers an explosion with a burst of collimated $\gamma$-rays. Following the initial prompt emission, some SGRBs exhibit a plateau phase in their $X$-ray light curves that indicates additional energy injection from a central engine, believed to be a rapidly rotating, highly magnetised neutron star. The collapse of this `protomagnetar' to a black hole is likely to be responsible for a steep decay in $X$-ray flux observed at the end of the plateau. In this letter, we show that these observations can be used to effectively constrain the equation of state of dense matter. In particular, we show that the known distribution of masses in binary neutron star systems, together with fits to the $X$-ray light curves, provide constraints that exclude the softest and stiffest plausible equations of state. We further illustrate how a future gravitational wave observation with Advanced LIGO/Virgo can place tight constraints on the equation of state, by adding into the picture a measurement of the chirp mass of the SGRB progenitor.Comment: accepted for publication in Phys. Rev.

Detection regimes of the cosmological gravitational wave background from astrophysical sources

Key targets for gravitational wave (GW) observatories, such as LIGO and the next generation interferometric detector, Advanced LIGO, include core-collapse of massive stars and the final stage of coalescence of compact stellar remnants. The combined GW signal from such events occurring throughout the Universe will produce an astrophysical GW background (AGB), one that is fundamentally different from the GW background by very early Universe processes. One can classify contributions to the AGB for different classes of sources based on the strength of the GW emissions from the individual sources, their peak emission frequency, emission duration and their event rate density distribution. This article provides an overview of the detectability regimes of the AGB in the context of current and planned gravitational wave observatories. We show that there are two important AGB signal detection regimes, which we define as `continuous' and `popcorn noise'. We describe how the `popcorn noise' AGB regime evolves with observation time and we discuss how this feature distinguishes it from the GW background produced from very early Universe processes.Comment: accepted for publication in New Astronomy Reviews; 23 pages and 2 figure

The Swift Gamma-Ray Burst redshift distribution: selection biases and optical brightness evolution at high-z?

We employ realistic constraints on astrophysical and instrumental selection effects to model the Gamma-Ray Burst (GRB) redshift distribution using {\it Swift} triggered redshift samples acquired from optical afterglows (OA) and the TOUGH survey. Models for the Malmquist bias, redshift desert, and the fraction of afterglows missing because of host galaxy dust extinction, are used to show how the "true" GRB redshift distribution is distorted to its presently observed biased distribution. We also investigate another selection effect arising from a correlation between $E_{{\rm iso}}$ and $L_{{\rm opt}}$. The analysis, which accounts for the missing fraction of redshifts in the two data subsets, shows that a combination of selection effects (both instrumental and astrophysical) can describe the observed GRB redshift distribution. Furthermore, the observed distribution is compatible with a GRB rate evolution that tracks the global SFR, although the rate at high-$z$ cannot be constrained with confidence. Taking selection effects into account, it is not necessary to invoke high-energy GRB luminosity evolution with redshift to explain the observed GRB rate at high-$z$.Comment: Version 2. Includes new data, figures and refined analysi