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Several methods have been proposed for performing schedulability analysis for both uni-processor and multi-processor real-time systems. Very few of these works use the power of formal logic to write unambiguous specifications and to allow the usage of theorem provers for building the proofs of interest with greater correctness guarantees. In this paper we address this challenge by: 1) defining a formal language that allows to specify periodic resource models; 2) describe a transformational approach to reasoning about timing properties of resource models by transforming the latter specifications into a satisfiability modulo theories problem.

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Over the past decades several approaches for schedulability analysis have been proposed for both uni-processor and multi-processor real-time systems. Although different techniques are employed, very little has been put forward in using formal specifications, with the consequent possibility for misinterpretations or ambiguities in the problem statement. Using a logic based approach to schedulability analysis in the design of hard real-time systems eases the synthesis of correct-byconstruction procedures for both static and dynamic verification processes. In this paper we propose a novel approach to schedulability analysis based on a timed temporal logic with time durations. Our approach subsumes classical methods for uniprocessor scheduling analysis over compositional resource models by providing the developer with counterexamples , and by ruling out schedules that cause unsafe violations on the system. We also provide an example showing the effectiveness of our proposal.

Runtime verification is an emerging discipline that investigates methods and tools to enable the verification of program properties during the execution of the application. The goal is to complement static analysis approaches, in particular when static verification leads to the explosion of states. Non-functional properties, such as the ones present in real-time systems are an ideal target for this kind of verification methodology, as are usually out of the range of the power and expressiveness of classic static analyses. In this paper, we present a framework that allows real-time programs written in Ada to be augmented with runtime verification capabilities. Our framework provides the infrastructures which is needed to instrument the code with runtime monitors. These monitors are responsible for observing the system and reaching verdicts about whether its behavior is compliant with its non-functional properties. We also sketch a contract language to extend the one currently provided by Ada, with the long term goal of having an elegant way in which runtime monitors can be automatically synthesized and instrumented into the target systems. The usefulness of the proposed approach is demonstrated by showing its use for an application scenario.