64.71.89.15 at 00:18, 10 December 2014

2014-12-10T00:18:06Z

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	~~In [[descriptive complexity]],~~ a ~~'''query'''~~ is ~~a mapping from structures of~~ one ~~[[signature (logic)\|signature]] to structures~~ of ~~another vocabulary~~. ~~[[Neil Immerman]],~~ in ~~his book "Descriptive Complexity", "use[s] the concept of query as the fundamental paradigm of computation" (p~~. ~~17).~~		The author is known as Araceli Gulledge. Interviewing is what I do for a residing but I strategy on changing it. To maintain birds is one of the things he enjoys most. For many years she's been living in Kansas.<br><br>Feel free to surf to my web site :: extended auto warranty [[http://owenphelps.com/UserProfile/tabid/355/userId/172983/Default.aspx linked web site]]

	~~Given signatures~~ <~~math~~>~~\sigma~~<~~/math~~> ~~and <math>\tau</math>, we define the set of~~ [[~~structure (mathematical logic)\|structure]]s on each language, <math>\mbox{STRUC}[\sigma]<~~/~~math> and <math>\mbox{STRUC}[\tau]<~~/~~math>~~. ~~A query is then any mapping~~
	~~<blockquote>~~
	~~<math>I : \mbox{STRUC}[\sigma] \to \mbox{STRUC}[\tau]<~~/~~math>~~
	</~~blockquote>~~
	~~[[Computational complexity theory]] can then be phrased in terms of the power of the mathematical logic necessary to express a given query.~~

	~~==Order-independent queries==~~

	A query is '''order-independent''' if the ordering of objects in the structure does not affect the results of the query. In databases, these queries correspond to [[generic query\|generic queries]] (Immerman 1999, p. 18).<!-- This isn't a great reference for this information, since it's in the "background" section. A reference that goes into more detail would be great. --> A query is order-independent iff <math> I(\mathfrak{A}) \equiv I(\mathfrak{B})</~~math> for any isomorphic structures <math>\mathfrak{A}<~~/~~math> and <math>\mathfrak{B}<~~/~~math>~~.



	~~==References==~~
	*{{cite book \| last = Immerman \| first = Neil \| authorlink = Neil Immerman \| title = Descriptive Complexity \| year = 1999 \| publisher = Springer-Verlag \| location = New York \| isbn = 0-387-98600-6}}

	~~{{comp-sci-theory-stub}}~~

	~~[[Category:Descriptive complexity~~]]

en>David Eppstein: unreferenced

2012-08-29T20:10:55Z

unreferenced

New page

In [[descriptive complexity]], a '''query''' is a mapping from structures of one [[signature (logic)|signature]] to structures of another vocabulary. [[Neil Immerman]], in his book "Descriptive Complexity", "use[s] the concept of query as the fundamental paradigm of computation" (p. 17).

Given signatures <math>\sigma</math> and <math>\tau</math>, we define the set of [[structure (mathematical logic)|structure]]s on each language, <math>\mbox{STRUC}[\sigma]</math> and <math>\mbox{STRUC}[\tau]</math>. A query is then any mapping
<blockquote>
<math>I : \mbox{STRUC}[\sigma] \to \mbox{STRUC}[\tau]</math>
</blockquote>
[[Computational complexity theory]] can then be phrased in terms of the power of the mathematical logic necessary to express a given query.

==Order-independent queries==

A query is '''order-independent''' if the ordering of objects in the structure does not affect the results of the query. In databases, these queries correspond to [[generic query|generic queries]] (Immerman 1999, p. 18). A query is order-independent iff <math> I(\mathfrak{A}) \equiv I(\mathfrak{B})</math> for any isomorphic structures <math>\mathfrak{A}</math> and <math>\mathfrak{B}</math>.

==References==
*{{cite book | last = Immerman | first = Neil | authorlink = Neil Immerman | title = Descriptive Complexity | year = 1999 | publisher = Springer-Verlag | location = New York | isbn = 0-387-98600-6}}

{{comp-sci-theory-stub}}

[[Category:Descriptive complexity]]

Three-dimensional graph - Revision history

64.71.89.15 at 00:18, 10 December 2014

en>David Eppstein: unreferenced