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marnikitta
commented
Nov 28, 2018
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| \begin{definition}{Nullification time} | ||
| of an input element $a_\tau$ is the time $\theta_{a_\tau}=inf(\hat{\tau}>\tau|W_{\hat{\tau}}\setminus{S_{\hat{\tau}}}\cap{Cl(D)(a_\tau)=\emptyset})$, where $Cl(D)$ is a transitive closure of the relation $D$. | ||
| of an input element $a_\tau$ is the first time $\theta_{a_tau}$ when all elements that are produced from the $a_\tau$ are in state or are released from the system. $\theta_{a_\tau}=inf(\hat{\tau}>\tau|W_{\hat{\tau}}\setminus{S_{\hat{\tau}}}\cap{Cl(D)(a_\tau)=\emptyset})$, where $Cl(D)$ is a transitive closure of the relation $D$. |
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Убойная формула, расписал словами ее перед тем как формулу давать
marnikitta
commented
Nov 28, 2018
| Within our model, one can define streaming system using only data flow elements and business logic. However, without the notion of time, we cannot observe any processing progress. Let $\tau\in{\mathbb{N}}$ be an exact global discrete time. Let $a_\tau\in{\Gamma}$ be the element, which enters at the time $\tau$, and $b_\tau\in{2^\Gamma}$ be the elements, which leave at the time $\tau$. Let $A_{\tau}=\bigcup\limits_{i=1}^{\tau}{a_i}$ be a set of all input elements by the time $\tau$ and ${B}_\tau=\bigcup\limits_{i=1}^{\tau}{b_i}$ be a set of all output elements. | ||
| Basically $D$ captures the notion of a logical graph which vertices are pure functions. | ||
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| Within our model, one can define streaming system using only data flow elements and business logic. However, without the notion of time, we cannot observe any processing progress. Let $\tau\in{\mathbb{N}}$ be an exact global discrete time. Let $a_\tau\in{\Gamma}$ be the element, which enters at the time $\tau$, and $b_\tau\in{2^\Gamma}$ be the elements, which leave at the time $\tau$. Let $A_{\tau}=\{a_i\}_{i=1}^{\tau}$ be a set of all input elements by the time $\tau$ and ${B}_\tau=\bigcup\limits_{i=1}^{\tau}{b_i}$ be a set of all output elements. |
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a_i - элемент множества. Объединять элементы не кошено. Объединяют множества.
marnikitta
commented
Nov 28, 2018
| \end{definition} | ||
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| Technically, states in existing stream processing systems are not data flow elements, but as it was mentioned above, they can be presented in such a way using drifting state model. The main purpose of the state is to accumulate the information about input items. Data flow elements cannot be in $W\setminus{S}$ for an infinite time by the definition. Hence, for each input element $a_\tau$, there is a nullification time $\theta_{a_\tau}$, thereafter all elements, which depend on $a_\tau$, are in the system state. Since the nullification time, the input element can affect output elements only through the state. | ||
| Technically, states in existing stream processing systems are not data flow elements, but as it was mentioned above, they can be presented in such a way using drifting state model. The main purpose of the state is to accumulate the information about input items. Data flow elements cannot stay in $W\setminus{S}$ for an infinite time by the definition. Hence, for each input element $a_\tau$, there is a nullification time $\theta_{a_\tau}$, thereafter all elements, which depend on $a_\tau$, are in the system state. Since the nullification time, the input element can affect output elements only through the state. |
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Что это за определение такое, что элементы не могут вечно сидеть в системе? По-хорошему, надо тогда вводить свойство прогресса в самом начале. А-ля "для любого a_i существует момент времени, когда он покинет систему"
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