Macro tree transducers are a combination of top-down tree transducers and macro grammars. They serve as a model for syntax-directed semantics in which context information can be handled. In this paper the formal model of macro tree transducers is studied by investigating typical automata theoretical topics like composition, decomposition, domains, and ranges of the induced translation classes. The extension with regular look-ahead is considered.

Swift monitoring of NGC 4151 with an∼6hr sampling over a total of 69 days in early 2016 is used to construct light curves covering five bands in the X-rays (0.3-50keV) and six in the ultraviolet (UV)/optical (1900-5500Å). The three hardest X-ray bands (>2.5keV) are all strongly correlated with no measurable interband lag,while the two softer bands show lower variability and weaker correlations. The UV/optical bands are significantly correlated with the X-rays, lagging ∼3-4days behind the hard X-rays. The variability within the UV/optical bands is also strongly correlated, with the UV appearing to lead the optical by ∼0.5-1days. This combination of 3day lags between the X-rays and UV and 1day lags within the UV/optical appears to rule out the "lamp-post" reprocessing model in which a hot, X-ray emitting corona directly illuminates the accretion disk, which then reprocesses the energy in the UV/optical. Instead, these results appear consistent with the Gardner & Done picture in which two separate reprocessings occur: first, emission from the corona illuminates an extreme-UV-emitting toroidal component that shields the disk from the corona; this then heats the extreme-UV component,which illuminates the disk and drives its variability.

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We investigate weighted finite automata over strings and strong bimonoids. Such algebraic structures satisfy the same laws as semirings except that no distributivity laws need to hold. We define two different behaviors and prove precise characterizations for them if the underlying strong bimonoid satisfies local finiteness conditions. Moreover, we show that in this case the given weighted automata can be determinized.

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