Merge branch 'master' of gitlab.odin.cse.buffalo.edu:ahuber/SketchingWorlds
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@ -84,6 +84,7 @@ We would like to argue that in the general case there is no computation of expec
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To this end, consider the following graph $G(V, E)$, where $|E| = m$, $|V| = \numTup$, and $i, j \in [\numTup]$. Consider the query $q_E(X_1,\ldots, X_\numTup) = \sum\limits_{(i, j) \in E} X_i \cdot X_j$.
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\AR{The two lemmas need to be re-written once notation for representing a query is finalized in Section 1.}
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\AH{\^-----This is an issue that we are currently discussing.}
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\begin{Lemma}\label{lem:const-p}
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If we can compute $\poly(\wElem_1,\ldots, \wElem_\numTup) = q_E(\wElem_1,\ldots, \wElem_\numTup)^3$ in T(m) time for $\wElem_1 = \ldots = \wElem_\numTup = \prob$, then we can count the number of 3-matchings in $G$ in $T(m) + O(m)$ time.
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\end{Lemma}
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@ -189,3 +190,5 @@ Then $\numocc{\tri}_2 = 0$, and if we can prove that\AR{Again you are not transc
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\end{itemize}
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we solve our problem for $q_E^3$ based on $G_2$ and we can compute $\numocc{\threedis}$, a hard problem.
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\end{proof}
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{\bf TESTING}
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$\vec{w}\sim\mathcal{D}$
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@ -2,11 +2,11 @@
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%!TEX root=./main.tex
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\section{Query translation into polynomials}
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\AH{This section will involve the set of queries (RA+) that we are interested in, the probabilistic/incomplete models we address, and the outer aggregate functions we perform over the output \textit{annotation}
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1) RA notation
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2) DB (TIDB) notation
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3) How queries translate into polynomials
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}
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%\AH{This section will involve the set of queries (RA+) that we are interested in, the probabilistic/incomplete models we address, and the outer aggregate functions we perform over the output \textit{annotation}
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%1) RA notation
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%2) DB (TIDB) notation
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%3) How queries translate into polynomials
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%}
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Given tables $\rel, \reli$, an arbitrary query $\query(\rel)$ over the positive relational operators (SPJU), abusing notation slightly denote the query polynomial as $\poly(X_1,\ldots, X_\numTup)$.
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\OK{
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