Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: In this work  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.  show that deciding whether a given \CSTN or CHyTN is dynamically consistent is \coNP-hard. Then,  offer a proof that deciding whether a given CHyTN is dynamically consistent is \PSPACE-hard, provided that the input instances are allod to include both multi-head and multi-tail hyperarcs. In light of this,  continue our study by focusing on CHyTNs that allow only multi-head or only multi-tail hyperarcs, and  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 beten CSTN{s}/CHyTN{s} and Mean Payoff Games. The presentation of the connection beten \CSTN{s}/CHyTNs and \MPG{s} is mediated by the \HTN model. In order to analyze the algorithm,  introduce a refined notion of dynamic-consistency, named $\epsilon$-dynamic-consistency, and present a sharp lor 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.
['Carlo Comin', 'Romeo Rizzi']
I am writing a research paper on a idea Checking Dynamic Consistency of Conditional Hyper Temporal Networks via Mean Payoff Games (Hardness and (pseudo) Singly-Exponential Time Algorithm)
[{"from": "human", "value": "I am writing a research paper on a idea Checking Dynamic Consistency of Conditional Hyper Temporal Networks via Mean Payoff Games (Hardness and (pseudo) Singly-Exponential Time Algorithm)"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: In this work  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.  show that deciding whether a given \\CSTN or CHyTN is dynamically consistent is \\coNP-hard. Then,  offer a proof that deciding whether a given CHyTN is dynamically consistent is \\PSPACE-hard, provided that the input instances are allod to include both multi-head and multi-tail hyperarcs. In light of this,  continue our study by focusing on CHyTNs that allow only multi-head or only multi-tail hyperarcs, and  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 beten CSTN{s}/CHyTN{s} and Mean Payoff Games. The presentation of the connection beten \\CSTN{s}/CHyTNs and \\MPG{s} is mediated by the \\HTN model. In order to analyze the algorithm,  introduce a refined notion of dynamic-consistency, named $\\epsilon$-dynamic-consistency, and present a sharp lor 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."}]