Abstract. GPUs are becoming a primary resource of computing power. They use a single instruction, multiple threads (SIMT) execution model that executes batches of threads in lockstep. If the control flow of threads within the same batch diverges, the different execution paths are scheduled sequentially; once the control flows reconverge, all threads are executed in lockstep again. Several thread batching mechanisms have been proposed, albeit without establishing their semantic validity or their scheduling properties. To increase the level of confidence in the correctness of GPU-accelerated programs, we formalize the SIMT execution model for a stack-based reconvergence mechanism in an operational semantics and prove its correctness by constructing a simulation between the SIMT semantics and a standard interleaved multi-thread semantics. We also demonstrate that the SIMT execution model produces unfair schedules in some cases. We discuss the problem of unfairness for different batching mechanisms like dynamic warp formation and a stack-less reconvergence strategy.
This chapter presents ForMoSA (FORmal MOdels and Safety Analysis), an integrated approach for the safety assessment of safety-critical embedded systems. The approach brings together the best of engineering practice, formal methods, and mathematics: traditional safety analysis, temporal logics and verification, as well as statistics and optimization. These three orthogonal techniques cover three different aspects of safety: fault tolerance, functional correctness, and quantitative analysis. The ForMoSA approach combines these techniques to assess system safety in a structured and formal way. Furthermore, the tight combination of methods from different analysis domains results in mutual benefits. The combined approach yields results which cannot be produced by any single technique on its own. The methodology was applied to several case studies from different industrial domains. One of them is an autonomous control of level crossings using radio-based communication, which is used in this chapter to describe the individual steps of the ForMoSA methodology.
We give an overview of the S# (pronounced "safety sharp") framework for rigorous, model-based analysis of safety-critical systems. We introduce S#'s expressive modeling language based on the C# programming language, showing how S#'s fault modeling and flexible model composition capabilities can be used to model a case study from the transportation sector with multiple design variants. A formal semantics for executable probabilistic models is given. Fully automated qualitative and quantitative safety analyses are conducted for the case study using algorithms of the model checkers LTSmin and MRMC. The results of the quantitative analyses are discussed in comparison with results obtained by using traditional techniques.
Keywords Safety analysis• Model checking • Quantitative analysis • Executable models • Formal methods B Johannes Leupolz
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