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

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Venue: | Journal of Computer and System Sciences |

Citations: | 50 - 4 self |

### BibTeX

@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...