Lower-bound Time-Complexity Analysis of Logic Programs

The paper proposes a technique for inferring conditions on goals that, when satisfied, ensure that a goal is sufficiently coarse-grained to warrant parallel evaluation. The method is powerful enough to reason about divide-and-conquer programs, and in the case of quicksort, for instance, can infer that a quicksort goal has a time complexity that exceeds 64 resolution steps (a threshold for spawning) if the input list is of length 10 or more. This gives a simple run-time tactic for controlling spawning. The method has been proved correct, can be implemented straightforwardly, has been demonstrated to be useful on a parallel machine, and, in contrast with much of the previous work on time-complexity analysis of logic programs, does not require any complicated difference equation solving machinery

Ant: A Framework for Increasing the Efficiency of Sequential Debugging Techniques with Parallel Programs

Bugs in sequential programs cost the software industry billions of dollars in lost productivity each year. Even if simple parallel programming models are created, they will not reduce the level of sequential bugs in programs below that of sequential programs. It can be argued that the complexity of current parallel programming models may increase the number of sequential bugs in parallel programs because they distract the programmer from the core logic of the program. Tools exist that identify statements related to sequential bugs and allow those bugs to be more quickly located and fixed. Their use in parallel programs will continue to be useful. Many of these debugging tools require runtime monitoring of program points of interest in a program and the overhead of this monitoring is usually very high. We propose Ant, a framework that increases the efficiency of sequential debugging techniques when used with parallel programs. The Ant framework takes two different strategies depending on whether the program to be debugged is a distributed memory program or shared memory program. For MPI programs, the Ant compiler analyzes the program and identifies two different types of code regions: those that all processes execute and regions that only part of the processes execute. For shared memory Pthreads programs, Ant uses a combination of static and dynamic analyses to determine similar parts of the program executing in parallel and the number of threads executing those parts of the program. The programs are instrumented with calls to Ant runtime libraries and debugging libraries based on the Ant compiler\u27s static analysis results. Relative to a naive port of a debugging tool (C-DIDUCE, in our cases), Ant\u27s technique, by exploiting the application\u27s parallelism, reduces the monitoring overhead by up to 15.85 times (and on average 9.23 times) for MPI programs executing with 32 processes and up to 18.14 times (and on average 8.73 times) for Pthreads programs executing with 8 threads, while maintaining high accuracy

Dynamic Complexity Meets Parameterised Algorithms

Dynamic Complexity studies the maintainability of queries with logical formulas in a setting where the underlying structure or database changes over time. Most often, these formulas are from first-order logic, giving rise to the dynamic complexity class DynFO. This paper investigates extensions of DynFO in the spirit of parameterised algorithms. In this setting structures come with a parameter k and the extensions allow additional "space" of size f(k) (in the form of an additional structure of this size) or additional time f(k) (in the form of iterations of formulas) or both. The resulting classes are compared with their non-dynamic counterparts and other classes. The main part of the paper explores the applicability of methods for parameterised algorithms to this setting through case studies for various well-known parameterised problems

Quantifying Resource Use in Computations

It is currently not possible to quantify the resources needed to perform a computation. As a consequence, it is not possible to reliably evaluate the hardware resources needed for the application of algorithms or the running of programs. This is apparent in both computer science, for instance, in cryptanalysis, and in neuroscience, for instance, comparative neuro-anatomy. A System versus Environment game formalism is proposed based on Computability Logic that allows to define a computational work function that describes the theoretical and physical resources needed to perform any purely algorithmic computation. Within this formalism, the cost of a computation is defined as the sum of information storage over the steps of the computation. The size of the computational device, eg, the action table of a Universal Turing Machine, the number of transistors in silicon, or the number and complexity of synapses in a neural net, is explicitly included in the computational cost. The proposed cost function leads in a natural way to known computational trade-offs and can be used to estimate the computational capacity of real silicon hardware and neural nets. The theory is applied to a historical case of 56 bit DES key recovery, as an example of application to cryptanalysis. Furthermore, the relative computational capacities of human brain neurons and the C. elegans nervous system are estimated as an example of application to neural nets.Comment: 26 pages, no figure