Template Generation - A Graph Profiling Algorithm

The availability of high-level design entry tooling is crucial for the viability of any reconfigurable SoC architecture. This paper presents a template generation algorithm. The objective of template generation step is to extract functional equivalent structures, i.e. templates, from a control data flow graph. By profiling the graph, the algorithm generates all the possible templates and the corresponding matches. Using unique serial numbers and circle numbers, the algorithm can find all distinct templates with multiple outputs. A new type of graph (hydragraph) that can cope with multiple outputs is introduced. The generated templates pepresented by the hydragraph are not limited in shapes, i.e., we can find templates with multiple outputs or multiple sinks

Ranking Templates for Linear Loops

We present a new method for the constraint-based synthesis of termination arguments for linear loop programs based on linear ranking templates. Linear ranking templates are parametrized, well-founded relations such that an assignment to the parameters gives rise to a ranking function. This approach generalizes existing methods and enables us to use templates for many different ranking functions with affine-linear components. We discuss templates for multiphase, piecewise, and lexicographic ranking functions. Because these ranking templates require both strict and non-strict inequalities, we use Motzkin's Transposition Theorem instead of Farkas Lemma to transform the generated $\exists\forall$-constraint into an $\exists$-constraint.Comment: TACAS 201

A Comparison of search templates for gravitational waves from binary inspiral

We compare the performances of the templates defined by three different types of approaches: traditional post-Newtonian templates (Taylor-approximants), ``resummed'' post-Newtonian templates assuming the adiabatic approximation and stopping before the plunge (P-approximants), and further ``resummed'' post-Newtonian templates going beyond the adiabatic approximation and incorporating the plunge with its transition from the inspiral (Effective-one-body approximants). The signal to noise ratio is significantly enhanced (mainly because of the inclusion of the plunge signal) by using these new effective-one-body templates relative to the usual post-Newtonian ones for binary masses greater than $30 M_\odot$, the most likely sources for initial laser interferometers. Independently of the question of the plunge signal, the comparison of the various templates confirms the usefulness of using resummation methods. The paper also summarizes the key elements of the construction of various templates and thus can serve as a resource for those involved in writing inspiral search software.Comment: eta-dependent tail terms corrected after related errata by Blanchet (2005

Computational Resources to Filter Gravitational Wave Data with P-approximant Templates

The prior knowledge of the gravitational waveform from compact binary systems makes matched filtering an attractive detection strategy. This detection method involves the filtering of the detector output with a set of theoretical waveforms or templates. One of the most important factors in this strategy is knowing how many templates are needed in order to reduce the loss of possible signals. In this study we calculate the number of templates and computational power needed for a one-step search for gravitational waves from inspiralling binary systems. We build on previous works by firstly expanding the post-Newtonian waveforms to 2.5-PN order and secondly, for the first time, calculating the number of templates needed when using P-approximant waveforms. The analysis is carried out for the four main first-generation interferometers, LIGO, GEO600, VIRGO and TAMA. As well as template number, we also calculate the computational cost of generating banks of templates for filtering GW data. We carry out the calculations for two initial conditions. In the first case we assume a minimum individual mass of $1 M_{\odot}$ and in the second, we assume a minimum individual mass of $5 M_{\odot}$. We find that, in general, we need more P-approximant templates to carry out a search than if we use standard PN templates. This increase varies according to the order of PN-approximation, but can be as high as a factor of 3 and is explained by the smaller span of the P-approximant templates as we go to higher masses. The promising outcome is that for 2-PN templates the increase is small and is outweighed by the known robustness of the 2-PN P-approximant templates.Comment: 17 pages, 8 figures, Submitted to Class.Quant.Gra