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Abstract. In the analysis of hybrid discrete-continuous systems, rich arithmetic constraint formulae with complex Boolean structure arise naturally. The iSAT algorithm, a solver for such formulae, is aimed at bounded model checking of hybrid systems. In this paper, we identify challenges emerging from planned and ongoing work to enhance the iSAT algorithm: First, we propose an extension of iSAT to directly handle ordinary differential equations as constraints. Second, we outline the recently introduced generalization of the iSAT algorithm to deal with probabilistic hybrid systems and some open research issues in that context. Third, we present ideas on how to move from bounded to unbounded model checking by using the concept of interpolation. Finally, we discuss the adaption of some parallelization techniques to the iSAT case, which will hopefully lead to performance gains in the future. By presenting these open research questions, this paper aims at fostering discussions on these extensions of constraint solving.

Due to the ever changing characteristics of the newly provided hardware, there is the permanent requirement of designing and redesigning software adequately to meet the basic hardware conditions. Especially for well-established software, easy portability of the functional as well as the non-functional properties, such as runtime performance or energy efficiency, would be beneficial, so that the software adapts automatically to the given hardware conditions. In this article, we explore the autotuning potential of several methods from scientific computing. In particular, we consider time-stepping methods and investigate the effect of relevant tuning parameters of the different methods. We also address the question, whether offline or online autotuning approaches are appropriate for the specific method. The methods from scientific computing considered are particle simulation methods, solution methods for differential equations, as well as sparse matrix computations. Index Terms-offline and online autotuning, performance analysis, portability of efficiency, time-stepping methods.

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