CARTESIAN PRODUCT PARTITIONING OF MULTI-DIMENSIONAL REACHABLE STATE SPACES

On Set Coverings in Cartesian Product Spaces

Partitioning State Spaces of Concurrent

As the model-checking becomes increasingly used in the industry as an analysis support, there is a big need for efficient new methods to deal with the large real-size of concurrent transition systems. We propose a new algorithm for partitioning the large state space modelling industrial designs as concurrent transition systems with hundreds of millions of states and transitions. The produced pa...

Infinite Dimensional Spaces and Cartesian Closedness

Infinite dimensional spaces frequently appear in physics; there are several approaches to obtain a good categorical framework for this type of space, and cartesian closedness of some category, embedding smooth manifolds, is one of the most requested condition. In the first part of the paper, we start from the failures presented by the classical Banach manifolds approach and we will review the m...

Prefibers and the cartesian product of metric spaces

Tardif, C., Prefibers and the Cartesian product of metric spaces, Discrete Mathematics 109 (1992) 283-288. The properties of certain sets called prefibers in a metric space are used to show that the algebraic properties of the Cartesian product of graphs generalize to metric spaces.

Data dependence theorems for operators on cartesian product spaces

We present some abstract data dependence theorems of the fixed point set for operators f, g : X × Y → X × Y , using the c-Picard operators technique. 2000 Mathematical Subject Classification: 47H10.