7,089 research outputs found
Inference of termination conditions for numerical loops
We present a new approach to termination analysis of numerical computations
in logic programs. Traditional approaches fail to analyse them due to non
well-foundedness of the integers. We present a technique that allows to
overcome these difficulties. Our approach is based on transforming a program in
way that allows integrating and extending techniques originally developed for
analysis of numerical computations in the framework of query-mapping pairs with
the well-known framework of acceptability. Such an integration not only
contributes to the understanding of termination behaviour of numerical
computations, but also allows to perform a correct analysis of such
computations automatically, thus, extending previous work on a
constraints-based approach to termination. In the last section of the paper we
discuss possible extensions of the technique, including incorporating general
term orderings.Comment: Presented at WST200
Active Learning of Multiple Source Multiple Destination Topologies
We consider the problem of inferring the topology of a network with
sources and receivers (hereafter referred to as an -by- network), by
sending probes between the sources and receivers. Prior work has shown that
this problem can be decomposed into two parts: first, infer smaller subnetwork
components (i.e., -by-'s or -by-'s) and then merge these components
to identify the -by- topology. In this paper, we focus on the second
part, which had previously received less attention in the literature. In
particular, we assume that a -by- topology is given and that all
-by- components can be queried and learned using end-to-end probes. The
problem is which -by-'s to query and how to merge them with the given
-by-, so as to exactly identify the -by- topology, and optimize a
number of performance metrics, including the number of queries (which directly
translates into measurement bandwidth), time complexity, and memory usage. We
provide a lower bound, , on the number of
-by-'s required by any active learning algorithm and propose two greedy
algorithms. The first algorithm follows the framework of multiple hypothesis
testing, in particular Generalized Binary Search (GBS), since our problem is
one of active learning, from -by- queries. The second algorithm is called
the Receiver Elimination Algorithm (REA) and follows a bottom-up approach: at
every step, it selects two receivers, queries the corresponding -by-, and
merges it with the given -by-; it requires exactly steps, which is
much less than all possible -by-'s. Simulation results
over synthetic and realistic topologies demonstrate that both algorithms
correctly identify the -by- topology and are near-optimal, but REA is
more efficient in practice
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