Weighted deduction systems provide a framework for describing parsing algorithms that can be used with a variety of operations for combining the values of partial derivations. For some operations, inside values can be computed efficiently, but outside values cannot. We view outside values as functions from inside values to the total value of all derivations, and we analyze outside computation in terms of function composition. This viewpoint helps explain why efficient outside computation is possible in many settings, despite the lack of a general outside algorithm for semiring operations.

中文翻译：

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高效的外部计算

加权推导系统提供了一个用于描述解析算法的框架，该算法可与用于组合部分推导值的各种操作一起使用。对于某些操作，可以有效地计算内部值，但不能有效地计算外部值。我们将外部值视为从内部值到所有派生总值的函数，并根据函数组合分析外部计算。这个观点有助于解释为什么在许多设置中可以进行高效的外部计算，尽管缺乏用于半环运算的通用外部算法。