Dyn-FO: A Parallel, Dynamic Complexity Class

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Dyn-FO: A Parallel, Dynamic Complexity Class (1994)

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by Sushant Patnaik , Neil Immerman

Venue:	Journal of Computer and System Sciences
Citations:	53 - 4 self

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@INPROCEEDINGS{Patnaik94dyn-fo:a,
    author = {Sushant Patnaik and Neil Immerman},
    title = {Dyn-FO: A Parallel, Dynamic Complexity Class},
    booktitle = {Journal of Computer and System Sciences},
    year = {1994},
    pages = {210--221}
}

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Abstract

Traditionally, computational complexity has considered only static problems. Classical Complexity Classes such as NC, P, and NP are defined in terms of the complexity of checking -- upon presentation of an entire input -- whether the input satisfies a certain property. For many applications of computers it is more appropriate to model the process as a dynamic one. There is a fairly large object being worked on over a period of time. The object is repeatedly modified by users and computations are performed. We develop a theory of Dynamic Complexity. We study the new complexity class, Dynamic First-Order Logic (Dyn-FO). This is the set of properties that can be maintained and queried in first-order logic, i.e. relational calculus, on a relational database. We show that many interesting properties are in Dyn-FO including multiplication, graph connectivity, bipartiteness, and the computation of minimum spanning trees. Note that none of these problems is in static FO, and this f...

Keyphrases

dynamic complexity class minimum spanning tree computational complexity entire input static problem new complexity class many application relational calculus classical complexity class dynamic complexity many interesting property relational database dynamic first-order logic certain property large object graph connectivity static fo first-order logic

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