004 Datenverarbeitung; Informatik
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Scheduling methodologies for real-time applications have been of keen interest to diverse research communities for several decades. Depending on the application area, algorithms have been developed that are tailored to specific requirements with respect to both the individual components of which an application is made up and the computational platform on which it is to be executed. Many real-time scheduling algorithms base their decisions solely or partly on timing constraints expressed by deadlines which must be met even under worst-case conditions. The increasing complexity of computing hardware means that worst-case execution time analysis becomes increasingly pessimistic. Scheduling hard real-time computations according to their worst-case execution times (which is common practice) will thus result, on average, in an increasing amount of spare capacity. The main goal of flexible real-time scheduling is to exploit this otherwise wasted capacity. Flexible scheduling schemes have been proposed to increase the ability of a real-time system to adapt to changing requirements and nondeterminism in the application behaviour. These models can be categorised as those whose source of flexibility is the quality of computations and those which are flexible regarding their timing constraints. This work describes a novel model which allows to specify both flexible timing constraints and quality profiles for an application. Furthermore, it demonstrates the applicability of this specification method to real-world examples and suggests a set of feasible scheduling algorithms for the proposed problem class.
One of the most important algorithms for real quantifier elimination is the quantifier elimination by virtual substitution introduced by Weispfenning in 1988. In this thesis we present numerous algorithmic approaches for optimizing this quantifier elimination algorithm. Optimization goals are the actual running time of the implementation of the algorithm and the size of the output formula. Strategies for obtaining these goals include simplification of first-order formulas,reduction of the size of the computed elimination set, and condensing a new replacement for the virtual substitution. Local quantifier elimination computes formulas that are equivalent to the input formula only nearby a given point. We can make use of this restriction for further optimizing the quantifier elimination by virtual substitution. Finally we discuss how to solve a large class of scheduling problems by real quantifier elimination. To optimize our algorithm for solving scheduling problems we make use of the special form of the input formula and of additional information given by the description of the scheduling problem