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Electronic Colloquium on Computational Complexity

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Reports tagged with alternating time:
TR04-020 | 8th March 2004
Emanuele Viola

The Complexity of Constructing Pseudorandom Generators from Hard Functions

We study the complexity of building
pseudorandom generators (PRGs) from hard functions.

We show that, starting from a function f : {0,1}^l -> {0,1} that
is mildly hard on average, i.e. every circuit of size 2^Omega(l)
fails to compute f on at least a 1/poly(l)
fraction of inputs, we can ... more >>>

TR05-137 | 21st November 2005
Emanuele Viola

On Probabilistic Time versus Alternating Time

We prove several new results regarding the relationship between probabilistic time, BPTime(t), and alternating time, \Sigma_{O(1)} Time(t). Our main results are the following:

1) We prove that BPTime(t) \subseteq \Sigma_3 Time(t polylog(t)). Previous results show that BPTime(t) \subseteq \Sigma_2 Time(t^2 log t) (Sipser and Gacs, STOC '83; Lautemann, IPL '83) ... more >>>

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