基于平均支付博弈的条件超时态网络动态一致性检验（硬度和（伪）单指数时间算法）
Checking Dynamic Consistency of Conditional Hyper Temporal Networks via Mean Payoff Games (Hardness and (pseudo) Singly-Exponential Time Algorithm)
摘要：
在这项工作中，我们介绍了\emph{Conditional Hyper Temporal Network (CHyTN)}模型，这是一个自然的扩展和推广的\CSTN和\HTN模型。我们的贡献如下。我们发现，决定是否一个给定的\CSTN或CHyTN是动态一致的是\coNP -硬。然后，我们提供了一个证明，决定是否一个给定的CHyTN是动态一致的是\PSPACE -硬，只要输入实例被允许包括多头和多尾超弧。有鉴于此，我们继续我们的研究集中在CHyTN只允许多头或只允许多尾超弧，我们提供了第一个确定性（伪）单指数时间算法的问题，检查动态一致性的CHyTN，也产生一个动态执行策略，只要输入CHyTN是动态一致的。由于\CSTN{s}是CHyTN的特殊情况，因此这提供了用于检查CSTN中的动态一致性的第一个健全且完整（伪）单指数时间算法作为副产品。该算法是基于一个新的连接之间的CNOW {s}/CHyTN{s}和平均支付游戏。\CSTN{s} /CHyTN和\MPG{s}之间的连接的呈现由\HTN模型介导。为了分析该算法，我们引入了一个精炼的概念，动态一致性，命名为$ε$ -动态一致性，并提出了一个尖锐的下界分析的反应时间的临界值$\hat{\varepsilon}$，其中一个\CSTN /CHyTN过渡，不被动态一致。在$\hat{\varepsilon}$的分析中引入的证明技术在处理包括严格不等式的线性差分约束时更普遍地适用。
英文摘要：
In this work we introduce the \emph{Conditional Hyper Temporal Network (CHyTN)} model, which is a natural extension and generalization of both the \CSTN and the \HTN model. Our contribution goes as follows. We show that deciding whether a given \CSTN or CHyTN is dynamically consistent is \coNP-hard. Then, we offer a proof that deciding whether a given CHyTN is dynamically consistent is \PSPACE-hard, provided that the input instances are allowed to include both multi-head and multi-tail hyperarcs. In light of this, we continue our study by focusing on CHyTNs that allow only multi-head or only multi-tail hyperarcs, and we offer the first deterministic (pseudo) singly-exponential time algorithm for the problem of checking the dynamic-consistency of such CHyTNs, also producing a dynamic execution strategy whenever the input CHyTN is dynamically consistent. Since \CSTN{s} are a special case of CHyTNs, this provides as a byproduct the first sound-and-complete (pseudo) singly-exponential time algorithm for checking dynamic-consistency in CSTNs. The proposed algorithm is based on a novel connection between CSTN{s}/CHyTN{s} and Mean Payoff Games. The presentation of the connection between \CSTN{s}/CHyTNs and \MPG{s} is mediated by the \HTN model. In order to analyze the algorithm, we introduce a refined notion of dynamic-consistency, named $ε$-dynamic-consistency, and present a sharp lower bounding analysis on the critical value of the reaction time $\hat{\varepsilon}$ where a \CSTN/CHyTN transits from being, to not being, dynamically consistent. The proof technique introduced in this analysis of $\hat{\varepsilon}$ is applicable more generally when dealing with linear difference constraints which include strict inequalities.
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