Abstract. The given paper conducts set-theoretic analysis of the structure of attributed transition systems with hidden transitions on the assumptions that the set of states for which the set of transitions can be extended is fixed and do not change the structure of the system. The cases are investigated where either priorities of hidden and available actions coincide or where the priority of hidden actions is higher than the priority of available actions. In terms of systems with selected initial and final states, the classes of admissible, safe, and correct systems are defined and characterized. The algebra of such systems is proposed.

Keywords: attributed transition systems, hidden transitions, admissibility, safeness and correctness of systems.