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...to G</math>. An example usage of this notion is that any two [[core (graph theory)|core]]s of a graph are homomorphically equivalent. ...the theory of [[database]]s. Given a [[database schema]], two [[instance (database)|instances]] ''I'' and ''J'' on it are called homomorphically equivalent if ...

...t previously made output, with the addition of new [[Tuple|tuples]] in the database. Formally, a query ''q'' over a schema ''R'' is monotonic if and only if fo ...uery processing may be optimized by executing only the new portions of the database and adding the new results to the existing answer set. ...

...lts. The two returned values will differ if <math>a</math> belongs to the database, and will be equal otherwise.{{r|gi}} ...n Cryptology – EUROCRYPT 2014: 33rd Annual International Conference on the Theory and Applications of Cryptographic Techniques, Copenhagen, Denmark, May 11-1 ...

...A table <math>T</math> is subject to a join [[dependency theory (database theory)|dependency]] if <math>T</math> can always be recreated by [[Relational_alg ...<math>R</math> itself.<ref>{{cite book|last=Silberschatz|first=Korth|title=Database System Concepts|edition=1st}}</ref> ...

...="Elmasri">{{cite book |last1=Elmasri |first1=Ramez |title=Fundamentals of database systems |date=2016 |publisher=Pearson |isbn=978-0133970777 |edition=Seventh ...nd <math>R_2</math>.<ref>{{cite book |last1=Maier |first1=David |title=The theory of relational databases |date=1983 |publisher=Computer Science Press |isbn= ...

...ref name="Libkin"/> The notion of certain answer, investigated in database theory since the 1970s,<ref name="Libkin"/> is indeed defined in the context of [[ * <math>D</math> is an incomplete database ...

In [[database theory|relational database theory]], an '''equality-generating dependency''' (EGD) is a certain kind of const [[Category:Database theory]] ...

...06-6 }}</ref> or '''RPQ''' is a query asking for pairs of endpoints in the database that are connected by a path satisfying a certain [[regular expression]]. A ...a [[regular expression]] over the set of labels. For instance, in a graph database where vertices represent users and there is an edge label "parent" for edge ...

...set of [[Functional dependency|functional dependencies]] on a [[Relation (database)|relation scheme]]) is a set of dependencies such that F [[logical implicat ...hive.org/web/20201108175024/https://mucse44.net/wp-content/uploads/2019/09/Database-System-Concepts-7th-Edition.pdf |archive-date=2020-11-08}}</ref> ...

...ting dependency''' (TGD) is a certain kind of constraint on a [[relational database]]. It is a subclass of the class of [[Embedded dependency|embedded dependen ...n [[first-order logic]] of the form:<ref>{{Cite book|title=Encyclopedia of Database Systems|url=https://archive.org/details/encyclopediadata00liul_180|url-acce ...

...intelligence]], [[knowledge representation and reasoning]], and [[database theory]] ...|website=il Quotidiano del Sud}}</ref> Previously, he was a professor of [[Database]] Systems at the [[TU Wien]].<ref>{{Cite web|url=https://www.dbai.tuwien.ac ...

...t=Yannakakis |first=Mihalis |date=1981-09-09 |title=Algorithms for acyclic database schemes |url=https://dl.acm.org/doi/10.5555/1286831.1286840 |journal=Procee Let <math>|D|</math> be the size of the database (i.e., the total number of tuples across all input relations), <math>|Q|</m ...

...s of the twenty-second ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems (PODS '03). ACM, New York, NY, USA, 202–210. [[DOI:10.1145/773153.7 ...th>, where each bit is the private information of a single individual. A ''database query'' is specified by a subset <math>S\subseteq \{1, \ldots, n\}</math>, ...

...s in [[database|database systems]]. It plays important roles in [[database theory]] as well as in practice. ...<ref>[[Alfred V. Aho]], [[Catriel Beeri]], and [[Jeffrey D. Ullman]]: "The Theory of Joins in Relational Databases", ACM Trans. Datab. Syst. 4(3):297-314, 19 ...

...edded dependency''' (ED) is a certain kind of constraint on a [[relational database]]. It is the most general type of constraint used in practice, including bo ...ce/article/pii/B9780444880741500226 |title=Elements of Relational Database Theory |last1=Kanellakis |first1=Paris C. |author-link1= |date=1990 |publisher=Els ...

...ast=Angles|first=Renzo|date=2012-04-01|title=A comparison of current graph database models|url=https://www.researchgate.net/publication/261076480|journal=Inter ...ertex (graph theory)|vertices]] represent entities and [[Glossary of graph theory#arc|arcs]] represent relationships. Each arc has an identifier, a source no ...

...|author2=Peter Høyer |title=Proceedings of the Fifth Israeli Symposium on Theory of Computing and Systems |chapter=An exact quantum polynomial-time algorith Assume we have an unsorted database with N elements, and an [[Oracle machine|oracle function]] <math>\chi</math ...

== Theory == ...in [[National Institute of Standards and Technology|NIST]] Atomic Spectra Database. It is often that [[Collisional radiative model|atomic modeling]]<ref>{{cit ...

...', 1955</ref><ref>A. Mood, F. Graybill, and D. Boes. ''Introduction to the Theory of Statistics''. McGraw-Hill, 3rd edition, 1974</ref>=== ...ath>P_{relevant}</math> be the set of relevant information elements in the database and <math>P_{retrieved}</math> be the set of the retrieved information elem ...

...active Database Privacy.In Proceedings of the 40th annual ACM symposium on Theory of computing, 2008]</ref> ...ly private manner and thus assure privacy to the individual records in the database <math>D\,\!</math>. ...