We prove that any AC0 circuit augmented with {epsilon log^2 n}
MOD_m gates and with a MAJORITY gate at the output, require size
n^{Omega(log n)} to compute MOD_l, when l has a prime
factor not dividing m and epsilon is sufficiently small. We
also obtain ... more >>>

NP-complete problems cannot have efficient algorithms unless P = NP. Due to their importance in practice, however, it is useful to improve the known exponential-time algorithms for NP-complete problems. We survey some of the recent results on such improved exponential-time algorithms for the NP-complete problems satisfiability, graph colorability, and the ... more >>>

This paper describes the Lempel-Ziv dimension (Hausdorff like
dimension inspired in the LZ78 parsing), its fundamental properties
and relation with Hausdorff dimension.

It is shown that in the case of individual infinite sequences, the
Lempel-Ziv dimension matches with the asymptotical Lempel-Ziv
compression ratio.

This fact is used to describe results ... more >>>