diff --git a/acknowledgements.tex b/acknowledgements.tex index c025e94..6fd24a9 100644 --- a/acknowledgements.tex +++ b/acknowledgements.tex @@ -1,3 +1,2 @@ %root: main.tex -\section{Acknowledgements} We thank Virginia Williams for showing us \Cref{eq:3p-3tri}, which greatly simplified our earlier proof of Lemma 3.8, and for graciously allowing us to use it. \ No newline at end of file diff --git a/app_approx-alg-analysis.tex b/app_approx-alg-analysis.tex index 3e4cac2..3f69ccc 100644 --- a/app_approx-alg-analysis.tex +++ b/app_approx-alg-analysis.tex @@ -94,7 +94,7 @@ For the claimed probability bound of $\probOf\left(\left|\vari{acc} - \rpoly(\pr This concludes the proof for the first claim of theorem~\ref{lem:mon-samp}. Next, we prove the claim on the runtime. \paragraph*{Run-time Analysis} -The runtime of the algorithm is dominated first by \Cref{alg:mon-sam-onepass} (which by \Cref{lem:one-pass} takes time $O\left({\size(\circuit)}\cdot \multc{\log\left(\abs{\circuit}(1,\ldots, 1)\right)}{\log\left(\size(\circuit)\right)}\right)$) and then by $\samplesize$ iterations of the loop in \Cref{alg:sampling-loop}. Each iteration's run time is dominated by the call to \sampmon in \Cref{alg:mon-sam-sample} (which by \Cref{lem:sample} takes $O\left(\log{k} \cdot k \cdot {\depth(\circuit)}\cdot \multc{\log\left(\abs{\circuit}(1,\ldots, 1)\right)}{\log\left(\size(\circuit)\right)}\right)$ +The runtime of the algorithm is dominated first by \Cref{alg:mon-sam-onepass} which has $O\left({\size(\circuit)}\cdot \multc{\log\left(\abs{\circuit}(1,\ldots, 1)\right)}{\log\left(\size(\circuit)\right)}\right)$ runtime by \Cref{lem:one-pass}. There are then $\samplesize$ iterations of the loop in \Cref{alg:sampling-loop}. Each iteration's run time is dominated by the call to \sampmon in \Cref{alg:mon-sam-sample} (which by \Cref{lem:sample} takes $O\left(\log{k} \cdot k \cdot {\depth(\circuit)}\cdot \multc{\log\left(\abs{\circuit}(1,\ldots, 1)\right)}{\log\left(\size(\circuit)\right)}\right)$ ) and the check \Cref{alg:check-duplicate-block}, which by the subsequent argument takes $O(k\log{k})$ time. We sort the $O(k)$ variables by their block IDs and then check if there is a duplicate block ID or not. Combining all the times discussed here gives us the desired overall runtime. \qed \end{proof} diff --git a/app_onepass-analysis.tex b/app_onepass-analysis.tex index afe6afe..9d2f898 100644 --- a/app_onepass-analysis.tex +++ b/app_onepass-analysis.tex @@ -90,7 +90,7 @@ When $\gate_{k+1}.\type = \circplus$, then by line~\ref{alg:one-pass-plus} $\gat When $\gate_{k+1}.\type = \circmult$, then line~\ref{alg:one-pass-mult} computes $\gate_{k+1}.\prt = \gate_{{k+1}_\lchild.\prt} \circmult \gate_{{k+1}_\rchild}.\prt$, which indeed by \cref{eq:T-all-ones} is correct. This concludes the proof of correctness. \paragraph*{Runtime Analysis} -It is known that $\topord(G)$ is computable in linear time. There are $\size(\circuit)$ iterations, each of which takes $O\left( \multc{\log\left(\abs{\circuit(1\ldots, 1)}\right)}{\log\inparen{\size(\circuit)}}\right)$ time. This can be seen since each of all the numbers which the algorithm computes is at most $\abs{\circuit}(1,\dots,1)$. Hence, by definition each such operation takes $\multc{\log\left(\abs{\circuit(1\ldots, 1)}\right)}{\log{\size(\circuit)}}$ time, which proves the claimed runtime. +It is known that $\topord(G)$ is computable in linear time. There are $\size(\circuit)$ iterations. Each iteration has runtime $O\left( \multc{\log\left(\abs{\circuit(1\ldots, 1)}\right)}{\log\inparen{\size(\circuit)}}\right)$ time. This can be seen since each of all the numbers which the algorithm computes is at most $\abs{\circuit}(1,\dots,1)$. Hence, by definition each such operation takes $\multc{\log\left(\abs{\circuit(1\ldots, 1)}\right)}{\log{\size(\circuit)}}$ time, which proves the claimed runtime. \qed \end{proof} diff --git a/app_set-to-bag-pdb.tex b/app_set-to-bag-pdb.tex index 59e3e6e..73cdc00 100644 --- a/app_set-to-bag-pdb.tex +++ b/app_set-to-bag-pdb.tex @@ -1,5 +1,6 @@ - +\onecolumn \section{Generalizing Beyond Set Inputs} + \label{sec:gener-results-beyond} \subsection{\abbrTIDB{}s} diff --git a/main.bbl b/main.bbl index 410f993..4fac178 100644 --- a/main.bbl +++ b/main.bbl @@ -1,285 +1,569 @@ -\begin{thebibliography}{10} +%%% -*-BibTeX-*- +%%% Do NOT edit. File created by BibTeX with style +%%% ACM-Reference-Format-Journals [18-Jan-2012]. -\bibitem{pdbench} -pdbench. -\newblock \url{http://pdbench.sourceforge.net/}. -\newblock Accessed: 2020-12-15. +\begin{thebibliography}{48} -\bibitem{DBLP:conf/vldb/AgrawalBSHNSW06} -Parag Agrawal, Omar Benjelloun, Anish~Das Sarma, Chris Hayworth, Shubha~U. - Nabar, Tomoe Sugihara, and Jennifer Widom. -\newblock Trio: A system for data, uncertainty, and lineage. -\newblock In {\em VLDB}, pages 1151--1154, 2006. +%%% ==================================================================== +%%% NOTE TO THE USER: you can override these defaults by providing +%%% customized versions of any of these macros before the \bibliography +%%% command. Each of them MUST provide its own final punctuation, +%%% except for \shownote{}, \showDOI{}, and \showURL{}. The latter two +%%% do not use final punctuation, in order to avoid confusing it with +%%% the Web address. +%%% +%%% To suppress output of a particular field, define its macro to expand +%%% to an empty string, or better, \unskip, like this: +%%% +%%% \newcommand{\showDOI}[1]{\unskip} % LaTeX syntax +%%% +%%% \def \showDOI #1{\unskip} % plain TeX syntax +%%% +%%% ==================================================================== -\bibitem{AB15} -Antoine Amarilli, Pierre Bourhis, and Pierre Senellart. -\newblock Probabilities and provenance via tree decompositions. -\newblock {\em PODS}, 2015. +\ifx \showCODEN \undefined \def \showCODEN #1{\unskip} \fi +\ifx \showDOI \undefined \def \showDOI #1{#1}\fi +\ifx \showISBNx \undefined \def \showISBNx #1{\unskip} \fi +\ifx \showISBNxiii \undefined \def \showISBNxiii #1{\unskip} \fi +\ifx \showISSN \undefined \def \showISSN #1{\unskip} \fi +\ifx \showLCCN \undefined \def \showLCCN #1{\unskip} \fi +\ifx \shownote \undefined \def \shownote #1{#1} \fi +\ifx \showarticletitle \undefined \def \showarticletitle #1{#1} \fi +\ifx \showURL \undefined \def \showURL {\relax} \fi +% The following commands are used for tagged output and should be +% invisible to TeX +\providecommand\bibfield[2]{#2} +\providecommand\bibinfo[2]{#2} +\providecommand\natexlab[1]{#1} +\providecommand\showeprint[2][]{arXiv:#2} -\bibitem{AD11d} -Yael Amsterdamer, Daniel Deutch, and Val Tannen. -\newblock Provenance for aggregate queries. -\newblock In {\em PODS}, pages 153--164, 2011. +\bibitem[pdb([n.\,d.])]% + {pdbench} + \bibinfo{year}{[n.\,d.]}\natexlab{}. +\newblock \bibinfo{title}{pdbench}. +\newblock \bibinfo{howpublished}{\url{http://pdbench.sourceforge.net/}}. +\newblock +\newblock +\shownote{Accessed: 2020-12-15}. -\bibitem{Antova_fastand} -Lyublena Antova, Thomas Jansen, Christoph Koch, and Dan Olteanu. -\newblock Fast and simple relational processing of uncertain data. -\bibitem{AGM} -Albert Atserias, Martin Grohe, and D{\'{a}}niel Marx. -\newblock Size bounds and query plans for relational joins. -\newblock {\em {SIAM} J. Comput.}, 42(4):1737--1767, 2013. -\newblock \href {https://doi.org/10.1137/110859440} - {\path{doi:10.1137/110859440}}. +\bibitem[Agrawal et~al\mbox{.}(2006)]% + {DBLP:conf/vldb/AgrawalBSHNSW06} +\bibfield{author}{\bibinfo{person}{Parag Agrawal}, \bibinfo{person}{Omar + Benjelloun}, \bibinfo{person}{Anish~Das Sarma}, \bibinfo{person}{Chris + Hayworth}, \bibinfo{person}{Shubha~U. Nabar}, \bibinfo{person}{Tomoe + Sugihara}, {and} \bibinfo{person}{Jennifer Widom}.} + \bibinfo{year}{2006}\natexlab{}. +\newblock \showarticletitle{Trio: A System for Data, Uncertainty, and Lineage}. + In \bibinfo{booktitle}{\emph{VLDB}}. \bibinfo{pages}{1151--1154}. +\newblock -\bibitem{bahar-93-al} -R.~Iris Bahar, Erica~A. Frohm, Charles~M. Gaona, Gary~D. Hachtel, Enrico Macii, - Abelardo Pardo, and Fabio Somenzi. -\newblock Algebraic decision diagrams and their applications. -\newblock In {\em IEEE CAD}, 1993. -\bibitem{DBLP:journals/pvldb/BeskalesIG10} -George Beskales, Ihab~F. Ilyas, and Lukasz Golab. -\newblock Sampling the repairs of functional dependency violations under hard - constraints. -\newblock {\em Proc. {VLDB} Endow.}, 3(1):197--207, 2010. +\bibitem[Amarilli et~al\mbox{.}(2015)]% + {AB15} +\bibfield{author}{\bibinfo{person}{Antoine Amarilli}, \bibinfo{person}{Pierre + Bourhis}, {and} \bibinfo{person}{Pierre Senellart}.} + \bibinfo{year}{2015}\natexlab{}. +\newblock \showarticletitle{Probabilities and provenance via tree + decompositions}. +\newblock \bibinfo{journal}{\emph{PODS}} (\bibinfo{year}{2015}). +\newblock -\bibitem{arith-complexity} -Peter Bürgisser, Michael Clausen, and Mohammad~Amin Shokrollahi. -\newblock {\em Algebraic complexity theory}, volume 315. -\newblock Springer, 1997. -\bibitem{chen-10-cswssr} -Hubie Chen and Martin Grohe. -\newblock Constraint satisfaction with succinctly specified relations. -\newblock {\em J. Comput. Syst. Sci.}, 76(8):847--860, 2010. +\bibitem[Amsterdamer et~al\mbox{.}(2011)]% + {AD11d} +\bibfield{author}{\bibinfo{person}{Yael Amsterdamer}, \bibinfo{person}{Daniel + Deutch}, {and} \bibinfo{person}{Val Tannen}.} + \bibinfo{year}{2011}\natexlab{}. +\newblock \showarticletitle{Provenance for Aggregate Queries}. In + \bibinfo{booktitle}{\emph{PODS}}. \bibinfo{pages}{153--164}. +\newblock -\bibitem{CHEN20061346} -Jianer Chen, Xiuzhen Huang, Iyad~A. Kanj, and Ge~Xia. -\newblock Strong computational lower bounds via parameterized complexity. -\newblock {\em Journal of Computer and System Sciences}, 72(8):1346--1367, - 2006. -\newblock URL: - \url{https://www.sciencedirect.com/science/article/pii/S0022000006000675}, - \href {https://doi.org/https://doi.org/10.1016/j.jcss.2006.04.007} - {\path{doi:https://doi.org/10.1016/j.jcss.2006.04.007}}. -\bibitem{k-match} -Radu Curticapean. -\newblock Counting matchings of size k is w[1]-hard. -\newblock In {\em ICALP}, volume 7965, pages 352--363, 2013. +\bibitem[Atserias et~al\mbox{.}(2013)]% + {AGM} +\bibfield{author}{\bibinfo{person}{Albert Atserias}, \bibinfo{person}{Martin + Grohe}, {and} \bibinfo{person}{D{\'{a}}niel Marx}.} + \bibinfo{year}{2013}\natexlab{}. +\newblock \showarticletitle{Size Bounds and Query Plans for Relational Joins}. +\newblock \bibinfo{journal}{\emph{{SIAM} J. Comput.}} \bibinfo{volume}{42}, + \bibinfo{number}{4} (\bibinfo{year}{2013}), \bibinfo{pages}{1737--1767}. +\newblock +\urldef\tempurl% +\url{https://doi.org/10.1137/110859440} +\showDOI{\tempurl} -\bibitem{DS07} -N.~Dalvi and D.~Suciu. -\newblock Efficient query evaluation on probabilistic databases. -\newblock {\em VLDB}, 16(4):544, 2007. -\bibitem{10.1145/1265530.1265571} -Nilesh Dalvi and Dan Suciu. -\newblock The dichotomy of conjunctive queries on probabilistic structures. -\newblock In {\em PODS}, pages 293--302, 2007. +\bibitem[Bahar et~al\mbox{.}(1993)]% + {bahar-93-al} +\bibfield{author}{\bibinfo{person}{R.~Iris Bahar}, \bibinfo{person}{Erica~A. + Frohm}, \bibinfo{person}{Charles~M. Gaona}, \bibinfo{person}{Gary~D. + Hachtel}, \bibinfo{person}{Enrico Macii}, \bibinfo{person}{Abelardo Pardo}, + {and} \bibinfo{person}{Fabio Somenzi}.} \bibinfo{year}{1993}\natexlab{}. +\newblock \showarticletitle{Algebraic decision diagrams and their + applications}. In \bibinfo{booktitle}{\emph{IEEE CAD}}. +\newblock -\bibitem{DS12} -Nilesh Dalvi and Dan Suciu. -\newblock The dichotomy of probabilistic inference for unions of conjunctive - queries. -\newblock {\em JACM}, 59(6):30, 2012. -\bibitem{heuvel-19-anappdsd} -Maarten~Van den Heuvel, Peter Ivanov, Wolfgang Gatterbauer, Floris Geerts, and - Martin Theobald. -\newblock Anytime approximation in probabilistic databases via scaled - dissociations. -\newblock In {\em SIGMOD}, pages 1295--1312, 2019. +\bibitem[Beskales et~al\mbox{.}(2010)]% + {DBLP:journals/pvldb/BeskalesIG10} +\bibfield{author}{\bibinfo{person}{George Beskales}, \bibinfo{person}{Ihab~F. + Ilyas}, {and} \bibinfo{person}{Lukasz Golab}.} + \bibinfo{year}{2010}\natexlab{}. +\newblock \showarticletitle{Sampling the Repairs of Functional Dependency + Violations under Hard Constraints}. +\newblock \bibinfo{journal}{\emph{Proc. {VLDB} Endow.}} \bibinfo{volume}{3}, + \bibinfo{number}{1} (\bibinfo{year}{2010}), \bibinfo{pages}{197--207}. +\newblock -\bibitem{DM14c} -Daniel Deutch, Tova Milo, Sudeepa Roy, and Val Tannen. -\newblock Circuits for datalog provenance. -\newblock In {\em ICDT}, pages 201--212, 2014. -\bibitem{feng:2021:sigmod:efficient} -Su~Feng, Boris Glavic, Aaron Huber, and Oliver Kennedy. -\newblock Efficient uncertainty tracking for complex queries with - attribute-level bounds. -\newblock In {\em SIGMOD}, 2021. +\bibitem[Bürgisser et~al\mbox{.}(1997)]% + {arith-complexity} +\bibfield{author}{\bibinfo{person}{Peter Bürgisser}, \bibinfo{person}{Michael + Clausen}, {and} \bibinfo{person}{Mohammad~Amin Shokrollahi}.} + \bibinfo{year}{1997}\natexlab{}. +\newblock \bibinfo{booktitle}{\emph{Algebraic complexity theory}}. + Vol.~\bibinfo{volume}{315}. +\newblock \bibinfo{publisher}{Springer}. +\newblock -\bibitem{feng:2019:sigmod:uncertainty} -Su~Feng, Aaron Huber, Boris Glavic, and Oliver Kennedy. -\newblock Uncertainty annotated databases - a lightweight approach for - approximating certain answers. -\newblock In {\em SIGMOD}, 2019. -\bibitem{FH12} -Robert Fink, Larisa Han, and Dan Olteanu. -\newblock Aggregation in probabilistic databases via knowledge compilation. -\newblock {\em PVLDB}, 5(5):490--501, 2012. +\bibitem[Chen and Grohe(2010)]% + {chen-10-cswssr} +\bibfield{author}{\bibinfo{person}{Hubie Chen} {and} \bibinfo{person}{Martin + Grohe}.} \bibinfo{year}{2010}\natexlab{}. +\newblock \showarticletitle{Constraint Satisfaction With Succinctly Specified + Relations}. +\newblock \bibinfo{journal}{\emph{J. Comput. Syst. Sci.}} \bibinfo{volume}{76}, + \bibinfo{number}{8} (\bibinfo{year}{2010}), \bibinfo{pages}{847--860}. +\newblock -\bibitem{FH13} -Robert Fink, Jiewen Huang, and Dan Olteanu. -\newblock Anytime approximation in probabilistic databases. -\newblock {\em VLDBJ}, 22(6):823--848, 2013. -\bibitem{FO16} -Robert Fink and Dan Olteanu. -\newblock Dichotomies for queries with negation in probabilistic databases. -\newblock {\em TODS}, 41(1):4:1--4:47, 2016. +\bibitem[Chen et~al\mbox{.}(2006)]% + {CHEN20061346} +\bibfield{author}{\bibinfo{person}{Jianer Chen}, \bibinfo{person}{Xiuzhen + Huang}, \bibinfo{person}{Iyad~A. Kanj}, {and} \bibinfo{person}{Ge Xia}.} + \bibinfo{year}{2006}\natexlab{}. +\newblock \showarticletitle{Strong computational lower bounds via parameterized + complexity}. +\newblock \bibinfo{journal}{\emph{J. Comput. System Sci.}} + \bibinfo{volume}{72}, \bibinfo{number}{8} (\bibinfo{year}{2006}), + \bibinfo{pages}{1346--1367}. +\newblock +\showISSN{0022-0000} +\urldef\tempurl% +\url{https://doi.org/10.1016/j.jcss.2006.04.007} +\showDOI{\tempurl} -\bibitem{10.5555/645413.652181} -J\"{o}rg Flum and Martin Grohe. -\newblock The parameterized complexity of counting problems. -\newblock In {\em Proceedings of the 43rd Symposium on Foundations of Computer - Science}, FOCS '02, page 538, USA, 2002. IEEE Computer Society. -\bibitem{param-comp} -J{\"{o}}rg Flum and Martin Grohe. -\newblock {\em Parameterized Complexity Theory}. -\newblock Texts in Theoretical Computer Science. An {EATCS} Series. Springer, - 2006. -\newblock \href {https://doi.org/10.1007/3-540-29953-X} - {\path{doi:10.1007/3-540-29953-X}}. +\bibitem[Curticapean(2013)]% + {k-match} +\bibfield{author}{\bibinfo{person}{Radu Curticapean}.} + \bibinfo{year}{2013}\natexlab{}. +\newblock \showarticletitle{Counting Matchings of Size k Is W[1]-Hard}. In + \bibinfo{booktitle}{\emph{ICALP}}, Vol.~\bibinfo{volume}{7965}. + \bibinfo{pages}{352--363}. +\newblock -\bibitem{DBLP:books/daglib/0020812} -Hector Garcia{-}Molina, Jeffrey~D. Ullman, and Jennifer Widom. -\newblock {\em Database systems - the complete book {(2.} ed.)}. -\newblock Pearson Education, 2009. -\bibitem{graetzer-08-un} -George Gr{\"a}tzer. -\newblock {\em Universal algebra}. -\newblock Springer Science \& Business Media, 2008. +\bibitem[Dalvi and Suciu(2007a)]% + {10.1145/1265530.1265571} +\bibfield{author}{\bibinfo{person}{Nilesh Dalvi} {and} \bibinfo{person}{Dan + Suciu}.} \bibinfo{year}{2007}\natexlab{a}. +\newblock \showarticletitle{The Dichotomy of Conjunctive Queries on + Probabilistic Structures}. In \bibinfo{booktitle}{\emph{PODS}}. + \bibinfo{pages}{293--302}. +\newblock -\bibitem{DBLP:conf/pods/GreenKT07} -Todd~J. Green, Gregory Karvounarakis, and Val Tannen. -\newblock Provenance semirings. -\newblock In {\em PODS}, pages 31--40, 2007. -\bibitem{GT06} -Todd~J Green and Val Tannen. -\newblock Models for incomplete and probabilistic information. -\newblock In {\em EDBT}, pages 278--296. 2006. +\bibitem[Dalvi and Suciu(2007b)]% + {DS07} +\bibfield{author}{\bibinfo{person}{N. Dalvi} {and} \bibinfo{person}{D. Suciu}.} + \bibinfo{year}{2007}\natexlab{b}. +\newblock \showarticletitle{Efficient query evaluation on probabilistic + databases}. +\newblock \bibinfo{journal}{\emph{VLDB}} \bibinfo{volume}{16}, + \bibinfo{number}{4} (\bibinfo{year}{2007}), \bibinfo{pages}{544}. +\newblock -\bibitem{Imielinski1989IncompleteII} -T.~Imielinski and W.~Lipski. -\newblock Incomplete information in relational databases. -\newblock 1989. -\bibitem{IL84a} -Tomasz Imieli\'nski and Witold Lipski~Jr. -\newblock Incomplete information in relational databases. -\newblock {\em JACM}, 31(4):761--791, 1984. +\bibitem[Dalvi and Suciu(2012)]% + {DS12} +\bibfield{author}{\bibinfo{person}{Nilesh Dalvi} {and} \bibinfo{person}{Dan + Suciu}.} \bibinfo{year}{2012}\natexlab{}. +\newblock \showarticletitle{The dichotomy of probabilistic inference for unions + of conjunctive queries}. +\newblock \bibinfo{journal}{\emph{JACM}} \bibinfo{volume}{59}, + \bibinfo{number}{6} (\bibinfo{year}{2012}), \bibinfo{pages}{30}. +\newblock -\bibitem{jha-12-pdwm} -Abhay~Kumar Jha and Dan Suciu. -\newblock Probabilistic databases with markoviews. -\newblock {\em PVLDB}, 5(11):1160--1171, 2012. -\bibitem{DBLP:journals/jal/KarpLM89} -Richard~M. Karp, Michael Luby, and Neal Madras. -\newblock Monte-carlo approximation algorithms for enumeration problems. -\newblock {\em J. Algorithms}, 10(3):429--448, 1989. +\bibitem[den Heuvel et~al\mbox{.}(2019)]% + {heuvel-19-anappdsd} +\bibfield{author}{\bibinfo{person}{Maarten~Van den Heuvel}, + \bibinfo{person}{Peter Ivanov}, \bibinfo{person}{Wolfgang Gatterbauer}, + \bibinfo{person}{Floris Geerts}, {and} \bibinfo{person}{Martin Theobald}.} + \bibinfo{year}{2019}\natexlab{}. +\newblock \showarticletitle{Anytime Approximation in Probabilistic Databases + via Scaled Dissociations}. In \bibinfo{booktitle}{\emph{SIGMOD}}. + \bibinfo{pages}{1295--1312}. +\newblock -\bibitem{kenig-13-nclexpdc} -Batya Kenig, Avigdor Gal, and Ofer Strichman. -\newblock A new class of lineage expressions over probabilistic databases - computable in p-time. -\newblock In {\em SUM}, volume 8078, pages 219--232, 2013. -\bibitem{kennedy:2010:icde:pip} -Oliver Kennedy and Christoph Koch. -\newblock Pip: A database system for great and small expectations. -\newblock In {\em ICDE}, 2010. +\bibitem[Deutch et~al\mbox{.}(2014)]% + {DM14c} +\bibfield{author}{\bibinfo{person}{Daniel Deutch}, \bibinfo{person}{Tova Milo}, + \bibinfo{person}{Sudeepa Roy}, {and} \bibinfo{person}{Val Tannen}.} + \bibinfo{year}{2014}\natexlab{}. +\newblock \showarticletitle{Circuits for Datalog Provenance}. In + \bibinfo{booktitle}{\emph{ICDT}}. \bibinfo{pages}{201--212}. +\newblock -\bibitem{DBLP:conf/pods/KhamisNR16} -Mahmoud~Abo Khamis, Hung~Q. Ngo, and Atri Rudra. -\newblock Faq: Questions asked frequently. -\newblock In {\em PODS}, pages 13--28, 2016. -\bibitem{triang-hard} -Tsvi Kopelowitz and Virginia~Vassilevska Williams. -\newblock Towards optimal set-disjointness and set-intersection data - structures. -\newblock In {\em ICALP}, volume 168, pages 74:1--74:16, 2020. +\bibitem[Feng et~al\mbox{.}(2021)]% + {feng:2021:sigmod:efficient} +\bibfield{author}{\bibinfo{person}{Su Feng}, \bibinfo{person}{Boris Glavic}, + \bibinfo{person}{Aaron Huber}, {and} \bibinfo{person}{Oliver Kennedy}.} + \bibinfo{year}{2021}\natexlab{}. +\newblock \showarticletitle{Efficient Uncertainty Tracking for Complex Queries + with Attribute-level Bounds}. In \bibinfo{booktitle}{\emph{SIGMOD}}. +\newblock -\bibitem{kumari:2016:qdb:communicating} -Poonam Kumari, Said Achmiz, and Oliver Kennedy. -\newblock Communicating data quality in on-demand curation. -\newblock In {\em QDB}, 2016. -\bibitem{ngo-survey} -Hung~Q. Ngo. -\newblock Worst-case optimal join algorithms: Techniques, results, and open - problems. -\newblock In {\em PODS}, 2018. +\bibitem[Feng et~al\mbox{.}(2019)]% + {feng:2019:sigmod:uncertainty} +\bibfield{author}{\bibinfo{person}{Su Feng}, \bibinfo{person}{Aaron Huber}, + \bibinfo{person}{Boris Glavic}, {and} \bibinfo{person}{Oliver Kennedy}.} + \bibinfo{year}{2019}\natexlab{}. +\newblock \showarticletitle{Uncertainty Annotated Databases - A Lightweight + Approach for Approximating Certain Answers}. In + \bibinfo{booktitle}{\emph{SIGMOD}}. +\newblock -\bibitem{skew} -Hung~Q. Ngo, Christopher Ré, and Atri Rudra. -\newblock Skew strikes back: new developments in the theory of join algorithms. -\newblock {\em SIGMOD Rec.}, 42(4):5--16, 2013. -\bibitem{DBLP:conf/icde/OlteanuHK10} -Dan Olteanu, Jiewen Huang, and Christoph Koch. -\newblock Approximate confidence computation in probabilistic databases. -\newblock In {\em ICDE}, pages 145--156, 2010. +\bibitem[Fink et~al\mbox{.}(2012)]% + {FH12} +\bibfield{author}{\bibinfo{person}{Robert Fink}, \bibinfo{person}{Larisa Han}, + {and} \bibinfo{person}{Dan Olteanu}.} \bibinfo{year}{2012}\natexlab{}. +\newblock \showarticletitle{Aggregation in probabilistic databases via + knowledge compilation}. +\newblock \bibinfo{journal}{\emph{PVLDB}} \bibinfo{volume}{5}, + \bibinfo{number}{5} (\bibinfo{year}{2012}), \bibinfo{pages}{490--501}. +\newblock -\bibitem{factorized-db} -Dan Olteanu and Maximilian Schleich. -\newblock Factorized databases. -\newblock {\em SIGMOD Rec.}, 45(2):5--16, 2016. -\bibitem{DBLP:journals/pvldb/RekatsinasCIR17} -Theodoros Rekatsinas, Xu~Chu, Ihab~F. Ilyas, and Christopher R{\'{e}}. -\newblock Holoclean: Holistic data repairs with probabilistic inference. -\newblock {\em Proc. {VLDB} Endow.}, 10(11):1190--1201, 2017. +\bibitem[Fink et~al\mbox{.}(2013)]% + {FH13} +\bibfield{author}{\bibinfo{person}{Robert Fink}, \bibinfo{person}{Jiewen + Huang}, {and} \bibinfo{person}{Dan Olteanu}.} + \bibinfo{year}{2013}\natexlab{}. +\newblock \showarticletitle{Anytime approximation in probabilistic databases}. +\newblock \bibinfo{journal}{\emph{VLDBJ}} \bibinfo{volume}{22}, + \bibinfo{number}{6} (\bibinfo{year}{2013}), \bibinfo{pages}{823--848}. +\newblock -\bibitem{roy-11-f} -Sudeepa Roy, Vittorio Perduca, and Val Tannen. -\newblock Faster query answering in probabilistic databases using read-once - functions. -\newblock In {\em ICDT}, 2011. -\bibitem{RS07} -C.~Ré and D.~Suciu. -\newblock Materialized views in probabilistic databases: for information - exchange and query optimization. -\newblock In {\em VLDB}, pages 51--62, 2007. +\bibitem[Fink and Olteanu(2016)]% + {FO16} +\bibfield{author}{\bibinfo{person}{Robert Fink} {and} \bibinfo{person}{Dan + Olteanu}.} \bibinfo{year}{2016}\natexlab{}. +\newblock \showarticletitle{Dichotomies for Queries with Negation in + Probabilistic Databases}. +\newblock \bibinfo{journal}{\emph{TODS}} \bibinfo{volume}{41}, + \bibinfo{number}{1} (\bibinfo{year}{2016}), \bibinfo{pages}{4:1--4:47}. +\newblock -\bibitem{DBLP:journals/vldb/SaRR0W0Z17} -Christopher~De Sa, Alexander Ratner, Christopher R{\'{e}}, Jaeho Shin, Feiran - Wang, Sen Wu, and Ce~Zhang. -\newblock Incremental knowledge base construction using deepdive. -\newblock {\em {VLDB} J.}, 26(1):81--105, 2017. -\bibitem{sen-10-ronfqevpd} -Prithviraj Sen, Amol Deshpande, and Lise Getoor. -\newblock Read-once functions and query evaluation in probabilistic databases. -\newblock {\em PVLDB}, 3(1):1068--1079, 2010. +\bibitem[Flum and Grohe(2002)]% + {10.5555/645413.652181} +\bibfield{author}{\bibinfo{person}{J\"{o}rg Flum} {and} \bibinfo{person}{Martin + Grohe}.} \bibinfo{year}{2002}\natexlab{}. +\newblock \showarticletitle{The Parameterized Complexity of Counting Problems}. + In \bibinfo{booktitle}{\emph{Proceedings of the 43rd Symposium on Foundations + of Computer Science}} \emph{(\bibinfo{series}{FOCS '02})}. + \bibinfo{publisher}{IEEE Computer Society}, \bibinfo{address}{USA}, + \bibinfo{pages}{538}. +\newblock +\showISBNx{0769518222} -\bibitem{S18a} -Pierre Senellart. -\newblock Provenance and probabilities in relational databases. -\newblock {\em SIGMOD Record}, 46(4):5--15, 2018. -\bibitem{valiant-79-cenrp} -Leslie~G. Valiant. -\newblock The complexity of enumeration and reliability problems. -\newblock {\em SIAM J. Comput.}, 8(3):410--421, 1979. +\bibitem[Flum and Grohe(2006)]% + {param-comp} +\bibfield{author}{\bibinfo{person}{J{\"{o}}rg Flum} {and} + \bibinfo{person}{Martin Grohe}.} \bibinfo{year}{2006}\natexlab{}. +\newblock \bibinfo{booktitle}{\emph{Parameterized Complexity Theory}}. +\newblock \bibinfo{publisher}{Springer}. +\newblock +\showISBNx{978-3-540-29952-3} +\urldef\tempurl% +\url{https://doi.org/10.1007/3-540-29953-X} +\showDOI{\tempurl} -\bibitem{VS17} -Guy Van~den Broeck and Dan Suciu. -\newblock Query processing on probabilistic data: A survey. -\newblock 2017. -\bibitem{virgi-survey} -Virginia~Vassilevska Williams. -\newblock Some open problems in fine-grained complexity. -\newblock {\em {SIGACT} News}, 49(4):29--35, 2018. -\newblock \href {https://doi.org/10.1145/3300150.3300158} - {\path{doi:10.1145/3300150.3300158}}. +\bibitem[Garcia{-}Molina et~al\mbox{.}(2009)]% + {DBLP:books/daglib/0020812} +\bibfield{author}{\bibinfo{person}{Hector Garcia{-}Molina}, + \bibinfo{person}{Jeffrey~D. Ullman}, {and} \bibinfo{person}{Jennifer Widom}.} + \bibinfo{year}{2009}\natexlab{}. +\newblock \bibinfo{booktitle}{\emph{Database systems - the complete book {(2.} + ed.)}}. +\newblock \bibinfo{publisher}{Pearson Education}. +\newblock + + +\bibitem[Green et~al\mbox{.}(2007)]% + {DBLP:conf/pods/GreenKT07} +\bibfield{author}{\bibinfo{person}{Todd~J. Green}, \bibinfo{person}{Gregory + Karvounarakis}, {and} \bibinfo{person}{Val Tannen}.} + \bibinfo{year}{2007}\natexlab{}. +\newblock \showarticletitle{Provenance semirings}. In + \bibinfo{booktitle}{\emph{PODS}}. \bibinfo{pages}{31--40}. +\newblock + + +\bibitem[Green and Tannen(2006)]% + {GT06} +\bibfield{author}{\bibinfo{person}{Todd~J Green} {and} \bibinfo{person}{Val + Tannen}.} \bibinfo{year}{2006}\natexlab{}. +\newblock \showarticletitle{Models for incomplete and probabilistic + information}. +\newblock In \bibinfo{booktitle}{\emph{EDBT}}. \bibinfo{pages}{278--296}. +\newblock + + +\bibitem[Imielinski and Lipski(1989)]% + {Imielinski1989IncompleteII} +\bibfield{author}{\bibinfo{person}{T. Imielinski} {and} \bibinfo{person}{W. + Lipski}.} \bibinfo{year}{1989}\natexlab{}. +\newblock \showarticletitle{Incomplete Information in Relational Databases}. +\newblock + + +\bibitem[Imieli\'nski and Lipski~Jr(1984)]% + {IL84a} +\bibfield{author}{\bibinfo{person}{Tomasz Imieli\'nski} {and} + \bibinfo{person}{Witold Lipski~Jr}.} \bibinfo{year}{1984}\natexlab{}. +\newblock \showarticletitle{Incomplete Information in Relational Databases}. +\newblock \bibinfo{journal}{\emph{JACM}} \bibinfo{volume}{31}, + \bibinfo{number}{4} (\bibinfo{year}{1984}), \bibinfo{pages}{761--791}. +\newblock + + +\bibitem[Jha and Suciu(2012)]% + {jha-12-pdwm} +\bibfield{author}{\bibinfo{person}{Abhay~Kumar Jha} {and} \bibinfo{person}{Dan + Suciu}.} \bibinfo{year}{2012}\natexlab{}. +\newblock \showarticletitle{Probabilistic Databases With Markoviews}. +\newblock \bibinfo{journal}{\emph{PVLDB}} \bibinfo{volume}{5}, + \bibinfo{number}{11} (\bibinfo{year}{2012}), \bibinfo{pages}{1160--1171}. +\newblock + + +\bibitem[Karp et~al\mbox{.}(1989)]% + {DBLP:journals/jal/KarpLM89} +\bibfield{author}{\bibinfo{person}{Richard~M. Karp}, \bibinfo{person}{Michael + Luby}, {and} \bibinfo{person}{Neal Madras}.} \bibinfo{year}{1989}\natexlab{}. +\newblock \showarticletitle{Monte-Carlo Approximation Algorithms for + Enumeration Problems}. +\newblock \bibinfo{journal}{\emph{J. Algorithms}} \bibinfo{volume}{10}, + \bibinfo{number}{3} (\bibinfo{year}{1989}), \bibinfo{pages}{429--448}. +\newblock + + +\bibitem[Kenig et~al\mbox{.}(2013)]% + {kenig-13-nclexpdc} +\bibfield{author}{\bibinfo{person}{Batya Kenig}, \bibinfo{person}{Avigdor Gal}, + {and} \bibinfo{person}{Ofer Strichman}.} \bibinfo{year}{2013}\natexlab{}. +\newblock \showarticletitle{A New Class of Lineage Expressions over + Probabilistic Databases Computable in P-Time}. In + \bibinfo{booktitle}{\emph{SUM}}, Vol.~\bibinfo{volume}{8078}. + \bibinfo{pages}{219--232}. +\newblock + + +\bibitem[Khamis et~al\mbox{.}(2016)]% + {DBLP:conf/pods/KhamisNR16} +\bibfield{author}{\bibinfo{person}{Mahmoud~Abo Khamis}, + \bibinfo{person}{Hung~Q. Ngo}, {and} \bibinfo{person}{Atri Rudra}.} + \bibinfo{year}{2016}\natexlab{}. +\newblock \showarticletitle{FAQ: Questions Asked Frequently}. In + \bibinfo{booktitle}{\emph{PODS}}. \bibinfo{pages}{13--28}. +\newblock + + +\bibitem[Kopelowitz and Williams(2020)]% + {triang-hard} +\bibfield{author}{\bibinfo{person}{Tsvi Kopelowitz} {and} + \bibinfo{person}{Virginia~Vassilevska Williams}.} + \bibinfo{year}{2020}\natexlab{}. +\newblock \showarticletitle{Towards Optimal Set-Disjointness and + Set-Intersection Data Structures}. In \bibinfo{booktitle}{\emph{ICALP}}, + Vol.~\bibinfo{volume}{168}. \bibinfo{pages}{74:1--74:16}. +\newblock + + +\bibitem[Kumari et~al\mbox{.}(2016)]% + {kumari:2016:qdb:communicating} +\bibfield{author}{\bibinfo{person}{Poonam Kumari}, \bibinfo{person}{Said + Achmiz}, {and} \bibinfo{person}{Oliver Kennedy}.} + \bibinfo{year}{2016}\natexlab{}. +\newblock \showarticletitle{Communicating Data Quality in On-Demand Curation}. + In \bibinfo{booktitle}{\emph{QDB}}. +\newblock + + +\bibitem[Ngo(2018)]% + {ngo-survey} +\bibfield{author}{\bibinfo{person}{Hung~Q. Ngo}.} + \bibinfo{year}{2018}\natexlab{}. +\newblock \showarticletitle{Worst-Case Optimal Join Algorithms: Techniques, + Results, and Open Problems}. In \bibinfo{booktitle}{\emph{PODS}}. +\newblock + + +\bibitem[Ngo et~al\mbox{.}(2013)]% + {skew} +\bibfield{author}{\bibinfo{person}{Hung~Q. Ngo}, \bibinfo{person}{Christopher + Ré}, {and} \bibinfo{person}{Atri Rudra}.} \bibinfo{year}{2013}\natexlab{}. +\newblock \showarticletitle{Skew strikes back: new developments in the theory + of join algorithms}. +\newblock \bibinfo{journal}{\emph{SIGMOD Rec.}} \bibinfo{volume}{42}, + \bibinfo{number}{4} (\bibinfo{year}{2013}), \bibinfo{pages}{5--16}. +\newblock + + +\bibitem[Olteanu et~al\mbox{.}(2010)]% + {DBLP:conf/icde/OlteanuHK10} +\bibfield{author}{\bibinfo{person}{Dan Olteanu}, \bibinfo{person}{Jiewen + Huang}, {and} \bibinfo{person}{Christoph Koch}.} + \bibinfo{year}{2010}\natexlab{}. +\newblock \showarticletitle{Approximate confidence computation in probabilistic + databases}. In \bibinfo{booktitle}{\emph{ICDE}}. \bibinfo{pages}{145--156}. +\newblock + + +\bibitem[Olteanu and Schleich(2016)]% + {factorized-db} +\bibfield{author}{\bibinfo{person}{Dan Olteanu} {and} + \bibinfo{person}{Maximilian Schleich}.} \bibinfo{year}{2016}\natexlab{}. +\newblock \showarticletitle{Factorized Databases}. +\newblock \bibinfo{journal}{\emph{SIGMOD Rec.}} \bibinfo{volume}{45}, + \bibinfo{number}{2} (\bibinfo{year}{2016}), \bibinfo{pages}{5--16}. +\newblock + + +\bibitem[Rekatsinas et~al\mbox{.}(2017)]% + {DBLP:journals/pvldb/RekatsinasCIR17} +\bibfield{author}{\bibinfo{person}{Theodoros Rekatsinas}, \bibinfo{person}{Xu + Chu}, \bibinfo{person}{Ihab~F. Ilyas}, {and} \bibinfo{person}{Christopher + R{\'{e}}}.} \bibinfo{year}{2017}\natexlab{}. +\newblock \showarticletitle{HoloClean: Holistic Data Repairs with Probabilistic + Inference}. +\newblock \bibinfo{journal}{\emph{Proc. {VLDB} Endow.}} \bibinfo{volume}{10}, + \bibinfo{number}{11} (\bibinfo{year}{2017}), \bibinfo{pages}{1190--1201}. +\newblock + + +\bibitem[Roy et~al\mbox{.}(2011)]% + {roy-11-f} +\bibfield{author}{\bibinfo{person}{Sudeepa Roy}, \bibinfo{person}{Vittorio + Perduca}, {and} \bibinfo{person}{Val Tannen}.} + \bibinfo{year}{2011}\natexlab{}. +\newblock \showarticletitle{Faster query answering in probabilistic databases + using read-once functions}. In \bibinfo{booktitle}{\emph{ICDT}}. +\newblock + + +\bibitem[Ré and Suciu(2007)]% + {RS07} +\bibfield{author}{\bibinfo{person}{C. Ré} {and} \bibinfo{person}{D. Suciu}.} + \bibinfo{year}{2007}\natexlab{}. +\newblock \showarticletitle{Materialized views in probabilistic databases: for + information exchange and query optimization}. In + \bibinfo{booktitle}{\emph{VLDB}}. \bibinfo{pages}{51--62}. +\newblock + + +\bibitem[Sa et~al\mbox{.}(2017)]% + {DBLP:journals/vldb/SaRR0W0Z17} +\bibfield{author}{\bibinfo{person}{Christopher~De Sa}, + \bibinfo{person}{Alexander Ratner}, \bibinfo{person}{Christopher R{\'{e}}}, + \bibinfo{person}{Jaeho Shin}, \bibinfo{person}{Feiran Wang}, + \bibinfo{person}{Sen Wu}, {and} \bibinfo{person}{Ce Zhang}.} + \bibinfo{year}{2017}\natexlab{}. +\newblock \showarticletitle{Incremental knowledge base construction using + DeepDive}. +\newblock \bibinfo{journal}{\emph{{VLDB} J.}} \bibinfo{volume}{26}, + \bibinfo{number}{1} (\bibinfo{year}{2017}), \bibinfo{pages}{81--105}. +\newblock + + +\bibitem[Sen et~al\mbox{.}(2010)]% + {sen-10-ronfqevpd} +\bibfield{author}{\bibinfo{person}{Prithviraj Sen}, \bibinfo{person}{Amol + Deshpande}, {and} \bibinfo{person}{Lise Getoor}.} + \bibinfo{year}{2010}\natexlab{}. +\newblock \showarticletitle{Read-Once Functions and Query Evaluation in + Probabilistic Databases}. +\newblock \bibinfo{journal}{\emph{PVLDB}} \bibinfo{volume}{3}, + \bibinfo{number}{1} (\bibinfo{year}{2010}), \bibinfo{pages}{1068--1079}. +\newblock + + +\bibitem[Senellart(2018)]% + {S18a} +\bibfield{author}{\bibinfo{person}{Pierre Senellart}.} + \bibinfo{year}{2018}\natexlab{}. +\newblock \showarticletitle{Provenance and Probabilities in Relational + Databases}. +\newblock \bibinfo{journal}{\emph{SIGMOD Record}} \bibinfo{volume}{46}, + \bibinfo{number}{4} (\bibinfo{year}{2018}), \bibinfo{pages}{5--15}. +\newblock + + +\bibitem[Valiant(1979)]% + {valiant-79-cenrp} +\bibfield{author}{\bibinfo{person}{Leslie~G. Valiant}.} + \bibinfo{year}{1979}\natexlab{}. +\newblock \showarticletitle{The Complexity of Enumeration and Reliability + Problems}. +\newblock \bibinfo{journal}{\emph{SIAM J. Comput.}} \bibinfo{volume}{8}, + \bibinfo{number}{3} (\bibinfo{year}{1979}), \bibinfo{pages}{410--421}. +\newblock + + +\bibitem[Van~den Broeck and Suciu(2017)]% + {VS17} +\bibfield{author}{\bibinfo{person}{Guy Van~den Broeck} {and} + \bibinfo{person}{Dan Suciu}.} \bibinfo{year}{2017}\natexlab{}. +\newblock \showarticletitle{Query Processing on Probabilistic Data: A Survey}. +\newblock (\bibinfo{year}{2017}). +\newblock + + +\bibitem[Williams(2018)]% + {virgi-survey} +\bibfield{author}{\bibinfo{person}{Virginia~Vassilevska Williams}.} + \bibinfo{year}{2018}\natexlab{}. +\newblock \showarticletitle{Some Open Problems in Fine-Grained Complexity}. +\newblock \bibinfo{journal}{\emph{{SIGACT} News}} \bibinfo{volume}{49}, + \bibinfo{number}{4} (\bibinfo{year}{2018}), \bibinfo{pages}{29--35}. +\newblock +\urldef\tempurl% +\url{https://doi.org/10.1145/3300150.3300158} +\showDOI{\tempurl} + + +\bibitem[Yang et~al\mbox{.}(2015)]% + {yang:2015:pvldb:lenses} +\bibfield{author}{\bibinfo{person}{Ying Yang}, \bibinfo{person}{Niccolò + Meneghetti}, \bibinfo{person}{Ronny Fehling}, \bibinfo{person}{Zhen~Hua Liu}, + \bibinfo{person}{Dieter Gawlick}, {and} \bibinfo{person}{Oliver Kennedy}.} + \bibinfo{year}{2015}\natexlab{}. +\newblock \showarticletitle{Lenses: An On-Demand Approach to ETL}. +\newblock \bibinfo{journal}{\emph{PVLDB}} \bibinfo{volume}{8}, + \bibinfo{number}{12} (\bibinfo{year}{2015}), \bibinfo{pages}{1578--1589}. +\newblock -\bibitem{yang:2015:pvldb:lenses} -Ying Yang, Niccolò Meneghetti, Ronny Fehling, Zhen~Hua Liu, Dieter Gawlick, - and Oliver Kennedy. -\newblock Lenses: An on-demand approach to etl. -\newblock {\em PVLDB}, 8(12):1578--1589, 2015. \end{thebibliography} diff --git a/main.bib b/main.bib index f18b012..4cded4e 100644 --- a/main.bib +++ b/main.bib @@ -1,3 +1,13 @@ +@INPROCEEDINGS{4497507, +author={Antova, Lyublena and Jansen, Thomas and Koch, Christoph and Olteanu, Dan}, +booktitle={2008 IEEE 24th International Conference on Data Engineering}, +title={Fast and Simple Relational Processing of Uncertain Data}, +year={2008}, +volume={}, +number={}, +pages={983-992}, +doi={10.1109/ICDE.2008.4497507}} + @article{CHEN20061346, title = {Strong computational lower bounds via parameterized complexity}, journal = {Journal of Computer and System Sciences}, @@ -119,12 +129,6 @@ Decompositions}, year = {2007} } -@misc{Antova_fastand, - author = {Lyublena Antova and Thomas Jansen and Christoph Koch and Dan Olteanu}, - title = {Fast and Simple Relational Processing of Uncertain Data}, - year = {} -} - @inproceedings{DBLP:conf/pods/KhamisNR16, author = {Mahmoud Abo Khamis and Hung Q. Ngo and diff --git a/main.out b/main.out index c131781..4e8a3b5 100644 --- a/main.out +++ b/main.out @@ -17,45 +17,44 @@ \BOOKMARK [1][-]{section.5}{\376\377\0005\000\040\000R\000e\000l\000a\000t\000e\000d\000\040\000W\000o\000r\000k}{}% 17 \BOOKMARK [1][-]{section.6}{\376\377\0006\000\040\000C\000o\000n\000c\000l\000u\000s\000i\000o\000n\000s\000\040\000a\000n\000d\000\040\000F\000u\000t\000u\000r\000e\000\040\000W\000o\000r\000k}{}% 18 \BOOKMARK [1][-]{section*.11}{\376\377\000A\000c\000k\000n\000o\000w\000l\000e\000d\000g\000m\000e\000n\000t\000s}{}% 19 -\BOOKMARK [1][-]{section.7}{\376\377\0007\000\040\000A\000c\000k\000n\000o\000w\000l\000e\000d\000g\000e\000m\000e\000n\000t\000s}{}% 20 -\BOOKMARK [1][-]{section*.13}{\376\377\000R\000e\000f\000e\000r\000e\000n\000c\000e\000s}{}% 21 -\BOOKMARK [1][-]{appendix.A}{\376\377\000A\000\040\000G\000e\000n\000e\000r\000a\000l\000i\000z\000i\000n\000g\000\040\000B\000e\000y\000o\000n\000d\000\040\000S\000e\000t\000\040\000I\000n\000p\000u\000t\000s}{}% 22 -\BOOKMARK [2][-]{subsection.A.1}{\376\377\000A\000.\0001\000\040\000T\000I\000D\000B\000s}{appendix.A}% 23 -\BOOKMARK [2][-]{subsection.A.2}{\376\377\000A\000.\0002\000\040\000B\000I\000D\000B\000s}{appendix.A}% 24 -\BOOKMARK [1][-]{appendix.B}{\376\377\000B\000\040\000M\000i\000s\000s\000i\000n\000g\000\040\000d\000e\000t\000a\000i\000l\000s\000\040\000f\000r\000o\000m\000\040\000S\000e\000c\000t\000i\000o\000n\000\040\0002}{}% 25 -\BOOKMARK [2][-]{subsection.B.1}{\376\377\000B\000.\0001\000\040\000K\000-\000r\000e\000l\000a\000t\000i\000o\000n\000s\000\040\000a\000n\000d\000\040\000N\000[\000X\000]\000-\000e\000n\000c\000o\000d\000e\000d\000\040\000P\000D\000B\000\040\000s}{appendix.B}% 26 -\BOOKMARK [2][-]{subsection.B.2}{\376\377\000B\000.\0002\000\040\000T\000I\000D\000B\000s\000\040\000a\000n\000d\000\040\000B\000I\000D\000B\000s\000\040\000i\000n\000\040\000t\000h\000e\000\040\000N\000[\000X\000]\000-\000e\000n\000c\000o\000d\000e\000d\000\040\000P\000D\000B\000\040\000m\000o\000d\000e\000l}{appendix.B}% 27 -\BOOKMARK [2][-]{subsection.B.3}{\376\377\000B\000.\0003\000\040\000P\000r\000o\000o\000f\000\040\000o\000f\000\040\000p\000r\000o\000p\000:\000e\000x\000p\000e\000c\000t\000i\000o\000n\000-\000o\000f\000-\000p\000o\000l\000y\000n\000o\000m}{appendix.B}% 28 -\BOOKMARK [2][-]{subsection.B.4}{\376\377\000B\000.\0004\000\040\000P\000r\000o\000p\000o\000s\000i\000t\000i\000o\000n\000\040\000B\000.\0004}{appendix.B}% 29 -\BOOKMARK [2][-]{subsection.B.5}{\376\377\000B\000.\0005\000\040\000P\000r\000o\000o\000f\000\040\000f\000o\000r\000\040\000L\000e\000m\000m\000a\000\040\0001\000.\0004}{appendix.B}% 30 -\BOOKMARK [2][-]{subsection.B.6}{\376\377\000B\000.\0006\000\040\000P\000r\000o\000o\000f\000\040\000F\000o\000r\000\040\000C\000o\000r\000o\000l\000l\000a\000r\000y\000\040\0002\000.\0007}{appendix.B}% 31 -\BOOKMARK [1][-]{appendix.C}{\376\377\000C\000\040\000M\000i\000s\000s\000i\000n\000g\000\040\000d\000e\000t\000a\000i\000l\000s\000\040\000f\000r\000o\000m\000\040\000S\000e\000c\000t\000i\000o\000n\000\040\0003}{}% 32 -\BOOKMARK [2][-]{subsection.C.1}{\376\377\000C\000.\0001\000\040\000l\000e\000m\000:\000p\000d\000b\000-\000f\000o\000r\000-\000d\000e\000f\000-\000q\000k}{appendix.C}% 33 -\BOOKMARK [2][-]{subsection.C.2}{\376\377\000C\000.\0002\000\040\000P\000r\000o\000o\000f\000\040\000o\000f\000\040\000l\000e\000m\000:\000t\000d\000e\000t\000-\000o\000m}{appendix.C}% 34 -\BOOKMARK [2][-]{subsection.C.3}{\376\377\000C\000.\0003\000\040\000l\000e\000m\000:\000q\000E\000k\000-\000m\000u\000l\000t\000i\000-\000p}{appendix.C}% 35 -\BOOKMARK [2][-]{subsection.C.4}{\376\377\000C\000.\0004\000\040\000P\000r\000o\000o\000f\000\040\000o\000f\000\040\000L\000e\000m\000m\000a\000\040\000C\000.\0002}{appendix.C}% 36 -\BOOKMARK [2][-]{subsection.C.5}{\376\377\000C\000.\0005\000\040\000P\000r\000o\000o\000f\000\040\000o\000f\000\040\000T\000h\000e\000o\000r\000e\000m\000\040\0003\000.\0006}{appendix.C}% 37 -\BOOKMARK [2][-]{subsection.C.6}{\376\377\000C\000.\0006\000\040\000S\000u\000b\000g\000r\000a\000p\000h\000\040\000N\000o\000t\000a\000t\000i\000o\000n\000\040\000a\000n\000d\000\040\000O\000\050\0001\000\051\000\040\000C\000l\000o\000s\000e\000d\000\040\000F\000o\000r\000m\000u\000l\000a\000s}{appendix.C}% 38 -\BOOKMARK [2][-]{subsection.C.7}{\376\377\000C\000.\0007\000\040\000P\000r\000o\000o\000f\000s\000\040\000o\000f\000\040\000e\000q\000:\0001\000e\000-\000e\000q\000:\0003\000p\000-\0003\000t\000r\000i}{appendix.C}% 39 -\BOOKMARK [2][-]{subsection.C.8}{\376\377\000C\000.\0008\000\040\000T\000o\000o\000l\000s\000\040\000t\000o\000\040\000p\000r\000o\000v\000e\000\040\000t\000h\000:\000s\000i\000n\000g\000l\000e\000-\000p\000-\000h\000a\000r\000d}{appendix.C}% 40 -\BOOKMARK [2][-]{subsection.C.9}{\376\377\000C\000.\0009\000\040\000P\000r\000o\000o\000f\000s\000\040\000f\000o\000r\000\040\000l\000e\000m\000:\0003\000m\000-\000G\0002\000,\000\040\000l\000e\000m\000:\000t\000r\000i\000,\000\040\000a\000n\000d\000\040\000l\000e\000m\000:\000l\000i\000n\000-\000s\000y\000s}{appendix.C}% 41 -\BOOKMARK [2][-]{subsection.C.10}{\376\377\000C\000.\0001\0000\000\040\000P\000r\000o\000o\000f\000\040\000o\000f\000\040\000t\000h\000:\000s\000i\000n\000g\000l\000e\000-\000p}{appendix.C}% 42 -\BOOKMARK [2][-]{subsection.C.11}{\376\377\000C\000.\0001\0001\000\040\000P\000r\000o\000o\000f\000\040\000o\000f\000\040\000t\000h\000:\000s\000i\000n\000g\000l\000e\000-\000p\000-\000h\000a\000r\000d}{appendix.C}% 43 -\BOOKMARK [1][-]{appendix.D}{\376\377\000D\000\040\000M\000i\000s\000s\000i\000n\000g\000\040\000D\000e\000t\000a\000i\000l\000s\000\040\000f\000r\000o\000m\000\040\000S\000e\000c\000t\000i\000o\000n\000\040\0004}{}% 44 -\BOOKMARK [2][-]{subsection.D.1}{\376\377\000D\000.\0001\000\040\000P\000r\000o\000o\000f\000\040\000o\000f\000\040\000T\000h\000e\000o\000r\000e\000m\000\040\000D\000.\0005}{appendix.D}% 45 -\BOOKMARK [2][-]{subsection.D.2}{\376\377\000D\000.\0002\000\040\000P\000r\000o\000o\000f\000\040\000o\000f\000\040\000T\000h\000e\000o\000r\000e\000m\000\040\000D\000.\0008}{appendix.D}% 46 -\BOOKMARK [2][-]{subsection.D.3}{\376\377\000D\000.\0003\000\040\000P\000r\000o\000o\000f\000\040\000o\000f\000\040\000c\000o\000r\000:\000a\000p\000p\000r\000o\000x\000-\000a\000l\000g\000o\000-\000c\000o\000n\000s\000t\000-\000p}{appendix.D}% 47 -\BOOKMARK [2][-]{subsection.D.4}{\376\377\000D\000.\0004\000\040\000P\000r\000o\000o\000f\000\040\000o\000f\000\040\000l\000e\000m\000:\000c\000t\000i\000d\000b\000-\000g\000a\000m\000m\000a}{appendix.D}% 48 -\BOOKMARK [2][-]{subsection.D.5}{\376\377\000D\000.\0005\000\040\000P\000r\000o\000o\000f\000\040\000o\000f\000\040\000l\000e\000m\000:\000v\000a\000l\000-\000u\000b}{appendix.D}% 49 -\BOOKMARK [2][-]{subsection.D.6}{\376\377\000D\000.\0006\000\040\000O\000n\000e\000P\000a\000s\000s\000\040\000R\000e\000m\000a\000r\000k\000s}{appendix.D}% 50 -\BOOKMARK [2][-]{subsection.D.7}{\376\377\000D\000.\0007\000\040\000O\000n\000e\000P\000a\000s\000s\000\040\000E\000x\000a\000m\000p\000l\000e}{appendix.D}% 51 -\BOOKMARK [2][-]{subsection.D.8}{\376\377\000D\000.\0008\000\040\000P\000r\000o\000o\000f\000\040\000o\000f\000\040\000O\000n\000e\000P\000a\000s\000s\000\040\000\050\000l\000e\000m\000:\000o\000n\000e\000-\000p\000a\000s\000s\000\051}{appendix.D}% 52 -\BOOKMARK [2][-]{subsection.D.9}{\376\377\000D\000.\0009\000\040\000S\000a\000m\000p\000l\000e\000M\000o\000n\000o\000m\000i\000a\000l\000\040\000R\000e\000m\000a\000r\000k\000s}{appendix.D}% 53 -\BOOKMARK [2][-]{subsection.D.10}{\376\377\000D\000.\0001\0000\000\040\000P\000r\000o\000o\000f\000\040\000o\000f\000\040\000S\000a\000m\000p\000l\000e\000M\000o\000n\000o\000m\000i\000a\000l\000\040\000\050\000l\000e\000m\000:\000s\000a\000m\000p\000l\000e\000\051}{appendix.D}% 54 -\BOOKMARK [2][-]{subsection.D.11}{\376\377\000D\000.\0001\0001\000\040\000E\000x\000p\000e\000r\000i\000m\000e\000n\000t\000a\000l\000\040\000R\000e\000s\000u\000l\000t\000s}{appendix.D}% 55 -\BOOKMARK [1][-]{appendix.E}{\376\377\000E\000\040\000C\000i\000r\000c\000u\000i\000t\000s}{}% 56 -\BOOKMARK [2][-]{subsection.E.1}{\376\377\000E\000.\0001\000\040\000R\000e\000p\000r\000e\000s\000e\000n\000t\000i\000n\000g\000\040\000P\000o\000l\000y\000n\000o\000m\000i\000a\000l\000s\000\040\000w\000i\000t\000h\000\040\000C\000i\000r\000c\000u\000i\000t\000s}{appendix.E}% 57 -\BOOKMARK [2][-]{subsection.E.2}{\376\377\000E\000.\0002\000\040\000M\000o\000d\000e\000l\000i\000n\000g\000\040\000C\000i\000r\000c\000u\000i\000t\000\040\000C\000o\000n\000s\000t\000r\000u\000c\000t\000i\000o\000n}{appendix.E}% 58 -\BOOKMARK [1][-]{appendix.F}{\376\377\000F\000\040\000H\000i\000g\000h\000e\000r\000\040\000M\000o\000m\000e\000n\000t\000s}{}% 59 -\BOOKMARK [1][-]{appendix.G}{\376\377\000G\000\040\000T\000h\000e\000\040\000K\000a\000r\000p\000-\000L\000u\000b\000y\000\040\000E\000s\000t\000i\000m\000a\000t\000o\000r}{}% 60 -\BOOKMARK [1][-]{appendix.H}{\376\377\000H\000\040\000P\000a\000r\000a\000m\000e\000t\000e\000r\000i\000z\000e\000d\000\040\000C\000o\000m\000p\000l\000e\000x\000i\000t\000y}{}% 61 +\BOOKMARK [1][-]{section*.13}{\376\377\000R\000e\000f\000e\000r\000e\000n\000c\000e\000s}{}% 20 +\BOOKMARK [1][-]{appendix.A}{\376\377\000A\000\040\000G\000e\000n\000e\000r\000a\000l\000i\000z\000i\000n\000g\000\040\000B\000e\000y\000o\000n\000d\000\040\000S\000e\000t\000\040\000I\000n\000p\000u\000t\000s}{}% 21 +\BOOKMARK [2][-]{subsection.A.1}{\376\377\000A\000.\0001\000\040\000T\000I\000D\000B\000s}{appendix.A}% 22 +\BOOKMARK [2][-]{subsection.A.2}{\376\377\000A\000.\0002\000\040\000B\000I\000D\000B\000s}{appendix.A}% 23 +\BOOKMARK [1][-]{appendix.B}{\376\377\000B\000\040\000M\000i\000s\000s\000i\000n\000g\000\040\000d\000e\000t\000a\000i\000l\000s\000\040\000f\000r\000o\000m\000\040\000S\000e\000c\000t\000i\000o\000n\000\040\0002}{}% 24 +\BOOKMARK [2][-]{subsection.B.1}{\376\377\000B\000.\0001\000\040\000K\000-\000r\000e\000l\000a\000t\000i\000o\000n\000s\000\040\000a\000n\000d\000\040\000N\000[\000X\000]\000-\000e\000n\000c\000o\000d\000e\000d\000\040\000P\000D\000B\000\040\000s}{appendix.B}% 25 +\BOOKMARK [2][-]{subsection.B.2}{\376\377\000B\000.\0002\000\040\000T\000I\000D\000B\000s\000\040\000a\000n\000d\000\040\000B\000I\000D\000B\000s\000\040\000i\000n\000\040\000t\000h\000e\000\040\000N\000[\000X\000]\000-\000e\000n\000c\000o\000d\000e\000d\000\040\000P\000D\000B\000\040\000m\000o\000d\000e\000l}{appendix.B}% 26 +\BOOKMARK [2][-]{subsection.B.3}{\376\377\000B\000.\0003\000\040\000P\000r\000o\000o\000f\000\040\000o\000f\000\040\000p\000r\000o\000p\000:\000e\000x\000p\000e\000c\000t\000i\000o\000n\000-\000o\000f\000-\000p\000o\000l\000y\000n\000o\000m}{appendix.B}% 27 +\BOOKMARK [2][-]{subsection.B.4}{\376\377\000B\000.\0004\000\040\000P\000r\000o\000p\000o\000s\000i\000t\000i\000o\000n\000\040\000B\000.\0004}{appendix.B}% 28 +\BOOKMARK [2][-]{subsection.B.5}{\376\377\000B\000.\0005\000\040\000P\000r\000o\000o\000f\000\040\000f\000o\000r\000\040\000L\000e\000m\000m\000a\000\040\0001\000.\0004}{appendix.B}% 29 +\BOOKMARK [2][-]{subsection.B.6}{\376\377\000B\000.\0006\000\040\000P\000r\000o\000o\000f\000\040\000F\000o\000r\000\040\000C\000o\000r\000o\000l\000l\000a\000r\000y\000\040\0002\000.\0007}{appendix.B}% 30 +\BOOKMARK [1][-]{appendix.C}{\376\377\000C\000\040\000M\000i\000s\000s\000i\000n\000g\000\040\000d\000e\000t\000a\000i\000l\000s\000\040\000f\000r\000o\000m\000\040\000S\000e\000c\000t\000i\000o\000n\000\040\0003}{}% 31 +\BOOKMARK [2][-]{subsection.C.1}{\376\377\000C\000.\0001\000\040\000l\000e\000m\000:\000p\000d\000b\000-\000f\000o\000r\000-\000d\000e\000f\000-\000q\000k}{appendix.C}% 32 +\BOOKMARK [2][-]{subsection.C.2}{\376\377\000C\000.\0002\000\040\000P\000r\000o\000o\000f\000\040\000o\000f\000\040\000l\000e\000m\000:\000t\000d\000e\000t\000-\000o\000m}{appendix.C}% 33 +\BOOKMARK [2][-]{subsection.C.3}{\376\377\000C\000.\0003\000\040\000l\000e\000m\000:\000q\000E\000k\000-\000m\000u\000l\000t\000i\000-\000p}{appendix.C}% 34 +\BOOKMARK [2][-]{subsection.C.4}{\376\377\000C\000.\0004\000\040\000P\000r\000o\000o\000f\000\040\000o\000f\000\040\000L\000e\000m\000m\000a\000\040\000C\000.\0002}{appendix.C}% 35 +\BOOKMARK [2][-]{subsection.C.5}{\376\377\000C\000.\0005\000\040\000P\000r\000o\000o\000f\000\040\000o\000f\000\040\000T\000h\000e\000o\000r\000e\000m\000\040\0003\000.\0006}{appendix.C}% 36 +\BOOKMARK [2][-]{subsection.C.6}{\376\377\000C\000.\0006\000\040\000S\000u\000b\000g\000r\000a\000p\000h\000\040\000N\000o\000t\000a\000t\000i\000o\000n\000\040\000a\000n\000d\000\040\000O\000\050\0001\000\051\000\040\000C\000l\000o\000s\000e\000d\000\040\000F\000o\000r\000m\000u\000l\000a\000s}{appendix.C}% 37 +\BOOKMARK [2][-]{subsection.C.7}{\376\377\000C\000.\0007\000\040\000P\000r\000o\000o\000f\000s\000\040\000o\000f\000\040\000e\000q\000:\0001\000e\000-\000e\000q\000:\0003\000p\000-\0003\000t\000r\000i}{appendix.C}% 38 +\BOOKMARK [2][-]{subsection.C.8}{\376\377\000C\000.\0008\000\040\000T\000o\000o\000l\000s\000\040\000t\000o\000\040\000p\000r\000o\000v\000e\000\040\000t\000h\000:\000s\000i\000n\000g\000l\000e\000-\000p\000-\000h\000a\000r\000d}{appendix.C}% 39 +\BOOKMARK [2][-]{subsection.C.9}{\376\377\000C\000.\0009\000\040\000P\000r\000o\000o\000f\000s\000\040\000f\000o\000r\000\040\000l\000e\000m\000:\0003\000m\000-\000G\0002\000,\000\040\000l\000e\000m\000:\000t\000r\000i\000,\000\040\000a\000n\000d\000\040\000l\000e\000m\000:\000l\000i\000n\000-\000s\000y\000s}{appendix.C}% 40 +\BOOKMARK [2][-]{subsection.C.10}{\376\377\000C\000.\0001\0000\000\040\000P\000r\000o\000o\000f\000\040\000o\000f\000\040\000t\000h\000:\000s\000i\000n\000g\000l\000e\000-\000p}{appendix.C}% 41 +\BOOKMARK [2][-]{subsection.C.11}{\376\377\000C\000.\0001\0001\000\040\000P\000r\000o\000o\000f\000\040\000o\000f\000\040\000t\000h\000:\000s\000i\000n\000g\000l\000e\000-\000p\000-\000h\000a\000r\000d}{appendix.C}% 42 +\BOOKMARK [1][-]{appendix.D}{\376\377\000D\000\040\000M\000i\000s\000s\000i\000n\000g\000\040\000D\000e\000t\000a\000i\000l\000s\000\040\000f\000r\000o\000m\000\040\000S\000e\000c\000t\000i\000o\000n\000\040\0004}{}% 43 +\BOOKMARK [2][-]{subsection.D.1}{\376\377\000D\000.\0001\000\040\000P\000r\000o\000o\000f\000\040\000o\000f\000\040\000T\000h\000e\000o\000r\000e\000m\000\040\000D\000.\0005}{appendix.D}% 44 +\BOOKMARK [2][-]{subsection.D.2}{\376\377\000D\000.\0002\000\040\000P\000r\000o\000o\000f\000\040\000o\000f\000\040\000T\000h\000e\000o\000r\000e\000m\000\040\000D\000.\0008}{appendix.D}% 45 +\BOOKMARK [2][-]{subsection.D.3}{\376\377\000D\000.\0003\000\040\000P\000r\000o\000o\000f\000\040\000o\000f\000\040\000c\000o\000r\000:\000a\000p\000p\000r\000o\000x\000-\000a\000l\000g\000o\000-\000c\000o\000n\000s\000t\000-\000p}{appendix.D}% 46 +\BOOKMARK [2][-]{subsection.D.4}{\376\377\000D\000.\0004\000\040\000P\000r\000o\000o\000f\000\040\000o\000f\000\040\000l\000e\000m\000:\000c\000t\000i\000d\000b\000-\000g\000a\000m\000m\000a}{appendix.D}% 47 +\BOOKMARK [2][-]{subsection.D.5}{\376\377\000D\000.\0005\000\040\000P\000r\000o\000o\000f\000\040\000o\000f\000\040\000l\000e\000m\000:\000v\000a\000l\000-\000u\000b}{appendix.D}% 48 +\BOOKMARK [2][-]{subsection.D.6}{\376\377\000D\000.\0006\000\040\000O\000n\000e\000P\000a\000s\000s\000\040\000R\000e\000m\000a\000r\000k\000s}{appendix.D}% 49 +\BOOKMARK [2][-]{subsection.D.7}{\376\377\000D\000.\0007\000\040\000O\000n\000e\000P\000a\000s\000s\000\040\000E\000x\000a\000m\000p\000l\000e}{appendix.D}% 50 +\BOOKMARK [2][-]{subsection.D.8}{\376\377\000D\000.\0008\000\040\000P\000r\000o\000o\000f\000\040\000o\000f\000\040\000O\000n\000e\000P\000a\000s\000s\000\040\000\050\000l\000e\000m\000:\000o\000n\000e\000-\000p\000a\000s\000s\000\051}{appendix.D}% 51 +\BOOKMARK [2][-]{subsection.D.9}{\376\377\000D\000.\0009\000\040\000S\000a\000m\000p\000l\000e\000M\000o\000n\000o\000m\000i\000a\000l\000\040\000R\000e\000m\000a\000r\000k\000s}{appendix.D}% 52 +\BOOKMARK [2][-]{subsection.D.10}{\376\377\000D\000.\0001\0000\000\040\000P\000r\000o\000o\000f\000\040\000o\000f\000\040\000S\000a\000m\000p\000l\000e\000M\000o\000n\000o\000m\000i\000a\000l\000\040\000\050\000l\000e\000m\000:\000s\000a\000m\000p\000l\000e\000\051}{appendix.D}% 53 +\BOOKMARK [2][-]{subsection.D.11}{\376\377\000D\000.\0001\0001\000\040\000E\000x\000p\000e\000r\000i\000m\000e\000n\000t\000a\000l\000\040\000R\000e\000s\000u\000l\000t\000s}{appendix.D}% 54 +\BOOKMARK [1][-]{appendix.E}{\376\377\000E\000\040\000C\000i\000r\000c\000u\000i\000t\000s}{}% 55 +\BOOKMARK [2][-]{subsection.E.1}{\376\377\000E\000.\0001\000\040\000R\000e\000p\000r\000e\000s\000e\000n\000t\000i\000n\000g\000\040\000P\000o\000l\000y\000n\000o\000m\000i\000a\000l\000s\000\040\000w\000i\000t\000h\000\040\000C\000i\000r\000c\000u\000i\000t\000s}{appendix.E}% 56 +\BOOKMARK [2][-]{subsection.E.2}{\376\377\000E\000.\0002\000\040\000M\000o\000d\000e\000l\000i\000n\000g\000\040\000C\000i\000r\000c\000u\000i\000t\000\040\000C\000o\000n\000s\000t\000r\000u\000c\000t\000i\000o\000n}{appendix.E}% 57 +\BOOKMARK [1][-]{appendix.F}{\376\377\000F\000\040\000H\000i\000g\000h\000e\000r\000\040\000M\000o\000m\000e\000n\000t\000s}{}% 58 +\BOOKMARK [1][-]{appendix.G}{\376\377\000G\000\040\000T\000h\000e\000\040\000K\000a\000r\000p\000-\000L\000u\000b\000y\000\040\000E\000s\000t\000i\000m\000a\000t\000o\000r}{}% 59 +\BOOKMARK [1][-]{appendix.H}{\376\377\000H\000\040\000P\000a\000r\000a\000m\000e\000t\000e\000r\000i\000z\000e\000d\000\040\000C\000o\000m\000p\000l\000e\000x\000i\000t\000y}{}% 60 diff --git a/main.pdf b/main.pdf index 5542b23..c634395 100644 Binary files a/main.pdf and b/main.pdf differ diff --git a/main.synctex.gz b/main.synctex.gz index 2ec2e3d..f97146b 100644 Binary files a/main.synctex.gz and b/main.synctex.gz differ