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arXiv 2103.05550cs.FLcs.GTcs.LO
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有限字上部分定义域的加权规格综合

Synthesis from Weighted Specifications with Partial Domains over Finite Words

Emmanuel Filiot, Christof Löding, Sarah Winter

摘要:

本文从定量指标出发研究了终止反应系统的综合问题。这种系统被建模为有限换能器,其执行被表示为$(I\times O)^*$中的有限字,其中$I,O$分别是输入和输出符号的有限集合。加权规格$S$分配一个有理值(或$-\infty$)到$(I\times O)^*$中的单词,并且我们考虑三种用于合成的目标,即阈值目标,其中系统的执行被要求高于某个给定阈值,最佳值和近似目标,其中要求系统通过提供产生最佳值和$\varepsilon$的输出符号来尽可能地执行。最佳值分别为w.r.t. $S$。我们建立了一个景观的可判定性的结果,这三个目标和加权规范与部分域的有限的话,由确定性加权自动机配备和,贴现和平均措施。由此产生的目标是不定期的一般情况下,我们开发了一个无限的游戏框架来解决相应的合成问题,即(加权)关键前缀游戏类。

英文摘要:

In this paper, we investigate the synthesis problem of terminating reactive systems from quantitative specifications. Such systems are modeled as finite transducers whose executions are represented as finite words in $(I\times O)^*$, where $I,O$ are finite sets of input and output symbols, respectively. A weighted specification $S$ assigns a rational value (or $-\infty$) to words in $(I\times O)^*$, and we consider three kinds of objectives for synthesis, namely threshold objectives where the system's executions are required to be above some given threshold, best-value and approximate objectives where the system is required to perform as best as it can by providing output symbols that yield the best value and $\varepsilon$-best value respectively w.r.t. $S$. We establish a landscape of decidability results for these three objectives and weighted specifications with partial domain over finite words given by deterministic weighted automata equipped with sum, discounted-sum and average measures. The resulting objectives are not regular in general and we develop an infinite game framework to solve the corresponding synthesis problems, namely the class of (weighted) critical prefix games.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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