Hybrid systems are a powerful formalism for modeling cyberphysical systems. Reachability analysis is a general method for checking safety properties, especially in the presence of uncertainty and nondeterminism. Rigorous simulation is a convenient tool for reachability analysis of hybrid systems. However, to serve as proof tool, a rigorous simulator must be correct wrt a clearly defined notion of reachability, which captures what is intuitively reachable in finite time. As a step towards addressing this challenge, this paper presents a rigorous simulator in the form of an operational semantics and a specification in the form of a denotational semantics. We show that, under certain conditions about the representation of enclosures, the rigorous simulator is correct. We also show that finding a representation satisfying these assumptions is non-trivial.
Recently, researchers' attention has been paid to pronunciation assessment not based on comparison between learners' utterances and native models, but based on comprehensibility of the utterances [1, 2, 3]. In our previous studies [4, 5], native listeners' shadowing was investigated and shown to be effective to predict comprehensibility perceived by listeners (shadowers). In this paper, native listeners' shadowings are viewed as spoken annotations that can represent comprehensibility. In [4, 5], to predict comprehensibility of a non-native utterance, the GOP scores of its corresponding native listeners' shadowings were calculated by using a DNN-based ASR front-end. Generally speaking, annotations are prepared manually and, even when some techniques are used for annotations, only stable and reliable techniques should be used. In this paper, a simpler, stabler, and more reliable method to derive comprehensibility annotations was proposed. After native listeners' shadowing, they are asked to read aloud the sentence intended by the learner. Reading is the most prepared speech and shadowing is probably the least prepared speech. DTW between the two utterances is supposed to be able to quantify and predict comprehensibility or shadowability perceived by the shadowers. In experiments, DTW between shadowings and readings shows higher correlation than the GOP scores of shadowings.
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