Estimating the computational cost of logic programs

Information about the computational cost of programs is potentially useful for a variety of purposes, including selecting among different algorithms, guiding program transformations, in granularity control and mapping decisions in parallelizing compilers, and query optimization in deductive databases. Cost analysis of logic programs is complicated by nondeterminism: on the one hand, procedures can return múltiple Solutions, making it necessary to estímate the number of solutions in order to give nontrivial upper bound cost estimates; on the other hand, the possibility of failure has to be taken into account while estimating lower bounds. Here we discuss techniques to address these problems to some extent.

Termination and cost analysis: Complexity and precision issues

The research in this thesis is related to static cost and termination analysis. Cost analysis aims at estimating the amount of resources that a given program consumes during the execution, and termination analysis aims at proving that the execution of a given program will eventually terminate. These analyses are strongly related, indeed cost analysis techniques heavily rely on techniques developed for termination analysis. Precision, scalability, and applicability are essential in static analysis in general. Precision is related to the quality of the inferred results, scalability to the size of programs that can be analyzed, and applicability to the class of programs that can be handled by the analysis (independently from precision and scalability issues). This thesis addresses these aspects in the context of cost and termination analysis, from both practical and theoretical perspectives. For cost analysis, we concentrate on the problem of solving cost relations (a form of recurrence relations) into closed-form upper and lower bounds, which is the heart of most modern cost analyzers, and also where most of the precision and applicability limitations can be found. We develop tools, and their underlying theoretical foundations, for solving cost relations that overcome the limitations of existing approaches, and demonstrate superiority in both precision and applicability. A unique feature of our techniques is the ability to smoothly handle both lower and upper bounds, by reversing the corresponding notions in the underlying theory. For termination analysis, we study the hardness of the problem of deciding termination for a speci�c form of simple loops that arise in the context of cost analysis. This study gives a better understanding of the (theoretical) limits of scalability and applicability for both termination and cost analysis.

Low cost 3D global instability analysis and flow sensitivity based on dynamic mode decomposition and high-order numerical tools

We explore the recently developed snapshot-based dynamic mode decomposition (DMD) technique, a matrix-free Arnoldi type method, to predict 3D linear global flow instabilities. We apply the DMD technique to flows confined in an L-shaped cavity and compare the resulting modes to their counterparts issued from classic, matrix forming, linear instability analysis (i.e. BiGlobal approach) and direct numerical simulations. Results show that the DMD technique, which uses snapshots generated by a 3D non-linear incompressible discontinuous Galerkin Navier?Stokes solver, provides very similar results to classical linear instability analysis techniques. In addition, we compare DMD results issued from non-linear and linearised Navier?Stokes solvers, showing that linearisation is not necessary (i.e. base flow not required) to obtain linear modes, as long as the analysis is restricted to the exponential growth regime, that is, flow regime governed by the linearised Navier?Stokes equations, and showing the potential of this type of analysis based on snapshots to general purpose CFD codes, without need of modifications. Finally, this work shows that the DMD technique can provide three-dimensional direct and adjoint modes through snapshots provided by the linearised and adjoint linearised Navier?Stokes equations advanced in time. Subsequently, these modes are used to provide structural sensitivity maps and sensitivity to base flow modification information for 3D flows and complex geometries, at an affordable computational cost. The information provided by the sensitivity study is used to modify the L-shaped geometry and control the most unstable 3D mode.

Rapid sizing tool for a low cost university microsatellite structure subsystem

In recent decays university class small satellites are creating many opportunities for space research and professional trainings while at the same time responding to constrained budgets. In this work the main focus is on developing a simple and rapid structural sizing tool considering the main objectives of a low cost university class microsatellite project. In satellite projects, structure subsystem is one of the influential subsystems as a driver of the cost and acceptance of the final design. At the first steps of such projects there is no confirmed data regarding the launch vehicle or even in some cases there is no data for the satellite payload. Due to these facts, developing simple sizing tools at conceptual design phase for obtaining an over view of the effect of different variables is useful before entering complex calculations in detailed design phases. In this study, after developing a simple analytical model of satellite structure subsystem, a design space is evaluated with practical boundaries considering mass and dimensions constraints of such projects. The results are useful to give initial insight to establish the system level structural sizing

Combining static analysis and profiling for estimating execution times

Effective static analyses have been proposed which infer bounds on the number of resolutions. These have the advantage of being independent from the platform on which the programs are executed and have been shown to be useful in a number of applications, such as granularity control in parallel execution. On the other hand, in distributed computation scenarios where platforms with different capabilities come into play, it is necessary to express costs in metrics that include the characteristics of the platform. In particular, it is specially interesting to be able to infer upper and lower bounds on actual execution times. With this objective in mind, we propose an approach which combines compile-time analysis for cost bounds with a one-time profiling of a given platform in order to determine the valúes of certain parameters for that platform. These parameters calibrate a cost model which, from then on, is able to compute statically time bound functions for procedures and to predict with a significant degree of accuracy the execution times of such procedures in that concrete platform. The approach has been implemented and integrated in the CiaoPP system.

Lower bound cost estimation for logic programs

It is generally recognized that information about the runtime cost of computations can be useful for a variety of applications, including program transformation, granularity control during parallel execution, and query optimization in deductive databases. Most of the work to date on compile-time cost estimation of logic programs has focused on the estimation of upper bounds on costs. However, in many applications, such as parallel implementations on distributed-memory machines, one would prefer to work with lower bounds instead. The problem with estimating lower bounds is that in general, it is necessary to account for the possibility of failure of head unification, leading to a trivial lower bound of 0. In this paper, we show how, given type and mode information about procedures in a logic program, it is possible to (semi-automatically) derive nontrivial lower bounds on their computational costs. We also discuss the cost analysis for the special and frequent case of divide-and-conquer programs and show how —as a pragmatic short-term solution —it may be possible to obtain useful results simply by identifying and treating divide-and-conquer programs specially.

Combining static analysis and profiling for estimating execution times in logic programs

Effective static analyses have been proposed which allow inferring functions which bound the number of resolutions or reductions. These have the advantage of being independent from the platform on which the programs are executed and such bounds have been shown useful in a number of applications, such as granularity control in parallel execution. On the other hand, in certain distributed computation scenarios where different platforms come into play, with each platform having different capabilities, it is more interesting to express costs in metrics that include the characteristics of the platform. In particular, it is specially interesting to be able to infer upper and lower bounds on actual execution time. With this objective in mind, we propose a method which allows inferring upper and lower bounds on the execution times of procedures of a program in a given execution platform. The approach combines compile-time cost bounds analysis with a one-time profiling of the platform in order to determine the values of certain constants for that platform. These constants calibrate a cost model which from then on is able to compute statically time bound functions for procedures and to predict with a significant degree of accuracy the execution times of such procedures in the given platform. The approach has been implemented and integrated in the CiaoPP system.

A Cost-Benefit analysis model for technical debt management considering uncertainty and time

In the last few years, technical debt has been used as a useful means for making the intrinsic cost of the internal software quality weaknesses visible. This visibility is made possible by quantifying this cost. Specifically, technical debt is expressed in terms of two main concepts: principal and interest. The principal is the cost of eliminating or reducing the impact of a, so called, technical debt item in a software system; whereas the interest is the recurring cost, over a time period, of not eliminating a technical debt item. Previous works about technical debt are mainly focused on estimating principal and interest, and on performing a cost-benefit analysis. This cost-benefit analysis allows one to determine if to remove technical debt is profitable and to prioritize which items incurring in technical debt should be fixed first. Nevertheless, for these previous works technical debt is flat along the time. However the introduction of new factors to estimate technical debt may produce non flat models that allow us to produce more accurate predictions. These factors should be used to estimate principal and interest, and to perform cost-benefit analysis related to technical debt. In this paper, we take a step forward introducing the uncertainty about the interest, and the time frame factors so that it becomes possible to depict a number of possible future scenarios. Estimations obtained without considering the possible evolution of the interest over time may be less accurate as they consider simplistic scenarios without changes.

Quick time planning using "s" curves and cost based durations.

ABSTRACT: The comparison of the different bids in the tender for a project, with the traditional contract system based on unit rates open to and re-measurement, requires analysis tools that are able to discriminate proposals having a similar overall economic impact, but that might show a very different behaviour during the execution of the works. RESUMEN: La estimación rápida de costes en fases iniciales del proyecto por métodos paramétricos y referencias estadísticas es un tema bien estudiado, divulgado y aplicado en el sector de la construcción. Sin embargo, existe poca literatura técnica sobre sistemas de predimensionado de tiempos, que permitan realizar rápidamente una planificación con un grado de aproximación razonable. Este texto reúne dos aspectos ya conocidos, pero hasta ahora independientes, y una aportación propia:  -La estimación del plazo final por referencias estadísticas (BCIS, 2000)  - La estimación del reparto del coste total a lo largo de la ejecución mediante curvas "S" (diversos autores)  La estimación de la duración de la ejecución de las actividades en función de su coste. El conjunto de estas tres técnicas, aplicadas a un proyecto, permite obtener una planificación con el suficiente grado de detalle y fiabilidad para tomar decisiones en fases iniciales del proyecto.

Development of Shape-Optimization Tools for the Aerodynamic Design of Turbomachinery Blades

The aim of this work is to develop an automated tool for the optimization of turbomachinery blades founded on an evolutionary strategy. This optimization scheme will serve to deal with supersonic blades cascades for application to Organic Rankine Cycle (ORC) turbines. The blade geometry is defined using parameterization techniques based on B-Splines curves, that allow to have a local control of the shape. The location in space of the control points of the B-Spline curve define the design variables of the optimization problem. In the present work, the performance of the blade shape is assessed by means of fully-turbulent flow simulations performed with a CFD package, in which a look-up table method is applied to ensure an accurate thermodynamic treatment. The solver is set along with the optimization tool to determine the optimal shape of the blade. As only blade-to-blade effects are of interest in this study, quasi-3D calculations are performed, and a single-objective evolutionary strategy is applied to the optimization. As a result, a non-intrusive tool, with no need for gradients definition, is developed. The computational cost is reduced by the use of surrogate models. A Gaussian interpolation scheme (Kriging model) is applied for the estimated n-dimensional function, and a surrogate-based local optimization strategy is proved to yield an accurate way for optimization. In particular, the present optimization scheme has been applied to the re-design of a supersonic stator cascade of an axial-flow turbine. In this design exercise very strong shock waves are generated in the rear blade suction side and shock-boundary layer interaction mechanisms occur. A significant efficiency improvement as a consequence of a more uniform flow at the blade outlet section of the stator is achieved. This is also expected to provide beneficial effects on the design of a subsequent downstream rotor. The method provides an improvement to gradient-based methods and an optimized blade geometry is easily achieved using the genetic algorithm.