We prove exponential lower bounds on the length of 2-query
locally decodable codes. Goldreich et al. recently proved such bounds
for the special case of linear locally decodable codes.
Our proof shows that a 2-query locally decodable code can be decoded
with only 1 quantum query, and then ... more >>>

We extend Lutz's measure to probabilistic classes, and obtain notions of measure on probabilistic complexity classes
C
such as BPP , BPE and BPEXP. Unlike former attempts,
all our measure notions satisfy all three Lutz's measure axioms, that is
every singleton {L} has measure zero ... more >>>

We discuss some connections between polynomial time and non-uniform, small depth circuits. A connection is shown with simulating deterministic time in small space. The well known result of Hopcroft, Paul and Valiant showing that space is more powerful than time can be improved, by making an assumption about the connection ... more >>>