Fluorescence interference contrast microscopy: Difference between revisions

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In [[computer science]], a '''first-order reduction''' is a very weak type of [[reduction (complexity)|reduction]] between two [[computational problem]]s in [[computational complexity theory]].  A first-order reduction is a reduction where each component is restricted to be in the class [[FO (complexity)|FO]] of problems calculable in [[first-order logic]].
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Since we have <math>\mbox{FO} \subsetneq \mbox{L}</math>, the first-order reductions are weaker reductions than the [[logspace reduction]]s.
 
Many important complexity classes are closed under first-order reductions, and many of the traditional [[complete (complexity)|complete]] problems are first-order complete as well (Immerman 1999 p. 49-50).  For example, [[ST-connectivity]] is FO-complete for [[NL (complexity)|NL]], and [[NL (complexity)|NL]] is closed under FO reductions (Immerman 1999, p. 51) (as are [[P (complexity)|P]], [[NP (complexity)|NP]], and most other "well-behaved" classes).
 
==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}}
 
[[Category:Descriptive complexity]]
 
{{comp-sci-stub}}

Latest revision as of 11:54, 25 October 2014

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