Abstract. For an
input of length N, we usually assume that the time complexity of any
algorithm is at least N, since the algorithm needs N steps only to read
the input. However, especially recently, there have been increasing
demands for studying algorithms that run in significantly less than N
steps by sacrificing the exactness of the computation. In this case, we
need some mechanism for algorithms to obtain the input, since it is no
longer possible to read all the input bits sequentially. "Oracles" are a
popular model for this purpose. The most standard oracle is socalled an
index oracle, that returns the ith bit of the input for the query i (an
integer between 1 and N). Thus, we obviously need N oracle calls in
order to get all the input bits in this case.
A little surprisingly, this is not always the case. For instance, some
Boolean functions can be computed, with high success probability, using
oracle calls much less than N times. Furthermore, if we are allowed to
use different kind of oracles or "quantum" oracles, then we can even
reconstruct the whole input string with less than N oracle calls. This
talk includes several interesting such cases and introduction to the
basic ideas and mechanisms making that possible.
