加权规划
Weighted Programming
摘要：
我们研究加权规划，指定数学模型的编程范式。更具体地说，我们研究的加权程序就像通常的命令式程序一样，具有两个额外的功能：（1）不确定性分支和（2）加权执行轨迹。权重可以是数字，也可以是其他对象，如字母表中的单词、多项式、形式幂级数或基数。我们认为，加权规划作为一种范式，可以用来指定数学模型超越概率分布（如概率规划）。我们开发了最弱的预条件和最弱的自由预条件风格的演算à la Dijkstra，用于推理加权程序指定的数学模型。我们提出了几个案例研究。例如，我们使用加权规划来模拟滑雪租赁问题-一个优化问题。我们不仅模型的优化问题本身，而且最好的确定性在线算法解决这个问题的加权程序。通过最弱前提式推理，可以在源代码级确定在线算法的竞争比。
英文摘要：
We study weighted programming, a programming paradigm for specifying mathematical models. More specifically, the weighted programs we investigate are like usual imperative programs with two additional features: (1) nondeterministic branching and (2) weighting execution traces. Weights can be numbers but also other objects like words from an alphabet, polynomials, formal power series, or cardinal numbers. We argue that weighted programming as a paradigm can be used to specify mathematical models beyond probability distributions (as is done in probabilistic programming). We develop weakest-precondition- and weakest-liberal-precondition-style calculi à la Dijkstra for reasoning about mathematical models specified by weighted programs. We present several case studies. For instance, we use weighted programming to model the ski rental problem - an optimization problem. We model not only the optimization problem itself, but also the best deterministic online algorithm for solving this problem as weighted programs. By means of weakest-precondition-style reasoning, we can determine the competitive ratio of the online algorithm on source code level.
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