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Generating Finite Integral Relation ...

Zhang, Si.

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Generating Finite Integral Relation Algebras.

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Generating Finite Integral Relation Algebras./
作者:	Zhang, Si.
面頁冊數:	74 p.
附註:	Source: Masters Abstracts International, Volume: 49-02, page: .
Contained By:	Masters Abstracts International49-02.
標題:	Computer Science. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=MR68198
ISBN:	9780494681985

Generating Finite Integral Relation Algebras.
Zhang, Si.

Generating Finite Integral Relation Algebras. - 74 p.

Source: Masters Abstracts International, Volume: 49-02, page: .

Thesis (M.Sc.)--Brock University (Canada), 2011.

Relation algebras and categories of relations in particular have proven to be extremely useful as a fundamental tool in mathematics and computer science. Since relation algebras are Boolean algebras with some well-behaved operations, every such algebra provides an atom structure, i.e., a relational structure on its set of atoms. In the case of complete and atomic structure (e.g. finite algebras), the original algebra can be recovered from its atom structure by using the complex algebra construction. This gives a representation of relation algebras as the complex algebra of a certain relational structure. This property is of particular interest because storing the atom structure requires less space than the entire algebra.

ISBN: 9780494681985Subjects--Topical Terms:

626642
Computer Science.

Generating Finite Integral Relation Algebras.
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520 $a Relation algebras and categories of relations in particular have proven to be extremely useful as a fundamental tool in mathematics and computer science. Since relation algebras are Boolean algebras with some well-behaved operations, every such algebra provides an atom structure, i.e., a relational structure on its set of atoms. In the case of complete and atomic structure (e.g. finite algebras), the original algebra can be recovered from its atom structure by using the complex algebra construction. This gives a representation of relation algebras as the complex algebra of a certain relational structure. This property is of particular interest because storing the atom structure requires less space than the entire algebra.
520 $a In this thesis I want to introduce and implement three structures representing atom structures of integral heterogeneous relation algebras, i.e., categorical versions of relation algebras. The first structure will simply embed a homogeneous atom structure of a relation algebra into the heterogeneous context. The second structure is obtained by splitting all symmetric idempotent relations. This new algebra is in almost all cases an heterogeneous structure having more objects than the original one. Finally, I will define two different union operations to combine two algebras into a single one.
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