The class NC$^1$ of problems solvable by bounded fan-in circuit families of logarithmic depth is known to be contained in logarithmic space L, but not much about the converse is known. In this paper we examine the structure of classes in between NC$^1$ and L based on counting functions or, ... more >>>

The deterministic space complexity of approximating the length of the longest increasing subsequence of
a stream of $N$ integers is known to be $\widetilde{\Theta}(\sqrt N)$. However, the randomized
complexity is wide open. We show that the technique used in earlier work to establish the $\Omega(\sqrt
N)$ deterministic lower bound fails ... more >>>

Recently in [Vij09, Corollary 3.7] the complexity class ModL has been shown to be closed under complement assuming NL = UL. In this note we continue to show many other closure properties of ModL which include the following.

1. ModL is closed under $\leq ^L_m$ reduction, $\vee$(join) and $\leq ^{UL}_m$ ... more >>>