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 >>>

The complexity class ModL was defined by Arvind and Vijayaraghavan in [AV04] (more precisely in Definition 1.4.1, Vij08],[Definition 3.1, AV]). In this paper, under the assumption that NL =UL, we show that for every language L\in ModL there exists a function f\in \sharpL and a function g\in FL such that ... more >>>

Given linear representations M_1 and M_2 of matroids over a field F, we consider the problem (denoted by ECLR), of checking if M_1 and M_2 represent the same matroid. We show that when F=Z_2, ECLR{Z_2} is complete for \parityL. Let M_1,M_2\in Q ^{m\times n} be two matroid linear representations given ... more >>>

The \emph{Orbit problem} is defined as follows: Given a matrix A\in \Q ^{n\times n} and vectors \x,\y\in \Q ^n, does there exist a
non-negative integer i such that A^i\x=\y. This problem was
shown to be in deterministic polynomial time by Kannan and Lipton in
\cite{KL1986}. In this paper we place ... more >>>

In this paper we study the complexity of Bounded Color
Multiplicity Graph Isomorphism (BCGI): the input is a pair of
vertex-colored graphs such that the number of vertices of a given
color in an input graph is bounded by b. We show that BCGI is in the
#L hierarchy ... more >>>