Index set
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In mathematics, the elements of a set A may be indexed or labeled by means of a set J that is on that account called an index set. The indexing consists of a surjective function from J onto A and the indexed collection is typically called an (indexed) family, often written as (Aj)j∈J.
In complexity theory and cryptography, an index set is a set for which there exists an algorithm I that can sample the set efficiently; i.e., on input 1n, I can efficiently select a poly(n)-bit long element from the set. [1]
[edit] Examples
- An enumeration of a set S gives an index set
, where 
is the particular enumeration of S.
- Any countably infinite set can be indexed by
.
- For
, the indicator function on r, is the function 
given by
The set of all the 
functions is an uncountable set indexed by 
.
[edit] References
- ^ Goldreich, Oded (2001). Foundations of Cryptography: Volume 1, Basic Tools. Cambridge University Press. ISBN 0-521-79172-3.
