Cubical token systems

The paper deals with combinatorial and stochastic structures of cubical token systems. A cubical token system is an instance of a token system, which in turn is an instance of a transition system. A formal theory based on a system of four independent axioms for cubical token systems and main algebraic properties of these systems are introduced. A representation theorem for a cubical token system is established asserting that the graph of such a system is cubical. Stationary distributions for random walks on cubical token systems are calculated.