Krzysztof Ziemiański

On execution spaces of PV-programs

Semaphores were introduced by Dijkstra as a tool for modeling concurrency in computer programs. In this paper we provide a formal definition of PV-programs, i.e. programs using semaphores, their state spaces and execution spaces. The main goal of this paper is to prove that every finite homotopy type may appear as a connected component of the execution space of a PV-program.

Homotopy representations of the unitary groups

Let

Homology of spaces of directed paths on Euclidean cubical complexes

G

Categories of directed spaces

be a compact connected Lie group and let

A cubical model for path spaces in d-simplicial complexes

\xi,\nu

A faithful unitary representation of the 2-compact group "DI"(4)

be complex vector bundles over the classifying space

Homotopy representations of SO(7) and Spin(7) at the prime 2

BG

Spaces of directed paths on pre-cubical sets

. The problem we consider is whether

Stable components of directed spaces

\xi

Directed suspensions and their loop spaces

contains a subbundle which is isomorphic to