In this paper we investigate the question whether a perfect matching can be isolated by a weighting scheme
using Chinese Remainder Theorem (short: CRT). We give a systematical analysis to a method based on CRT
suggested by Agrawal in a CCC'03-paper
for testing perfect matchings. We show that ... more >>>

In the present paper we show some new complexity bounds for
the matching problem for special graph classes.
We show that for graphs with a polynomially bounded number
of nice cycles, the decision perfect matching problem is in
$SPL$, it is hard for $FewL$, and the construction ... more >>>

The perfect matching problem is known to
be in P, in randomized NC, and it is hard for NL.
Whether the perfect matching problem is in NC is one of
the most prominent open questions in complexity
theory regarding parallel computations.

Grigoriev and Karpinski studied the perfect matching problem
more >>>

We show necessary and sufficient conditions that
certain algebraic functions like the rank or the signature
of an integer matrix can be computed in GapL.

We investigate the computational complexity
of the minimal polynomial of an integer matrix.

We show that the computation of the minimal polynomial
is in AC^0(GapL), the AC^0-closure of the logspace
counting class GapL, which is contained in NC^2.
Our main result is that the problem is hard ... more >>>