Branching Bisimilarity on Normed BPA Is EXPTIME-complete

We put forward an exponential-time algorithm for deciding branching bisimilarity on normed BPA (Bacis Process Algebra) systems. The decidability of branching (or weak) bisimilarity on normed BPA was once a long standing open problem which was closed by Yuxi Fu. The EXPTIME-hardness is an inference of a slight modification of the reduction presented by Richard Mayr. Our result claims that this problem is EXPTIME-complete.Comment: We correct many typing errors, add several remarks and an interesting toy exampl

Symmetric Subgroup Actions on Isotropic Grassmannians

Let G be the group preserving a nondegenerate sesquilinear form on a vector space V, and H a symmetric subgroup of G of the type G1 x G2. We explicitly parameterize the H-orbits in the Grassmannian of r-dimensional isotropic subspaces of V by a complete set of H-invariants. We describe the Bruhat order in terms of the majorization relationship over a diagram of these H-invariants. The inclusion order, the stabilizer, the orbit dimension, the open H-orbits, the decompositions of an H orbit into H\cap G_0 and H_0 orbits are also explicitly described.Comment: 30 page

Bicyclic graphs with exactly two main signless Laplacian eigenvalues

A signless Laplacian eigenvalue of a graph $G$ is called a main signless Laplacian eigenvalue if it has an eigenvector the sum of whose entries is not equal to zero. In this paper, all connected bicyclic graphs with exactly two main eigenvalues are determined