Probabilistic graph-theoretic models for dynamic and information capability problems research

We consider the system's functioning such that this functioning is fulfilled according to the given network of operations (i.e., according to the provided plan) but can be alternated due to impact of the environment. The impact of the environment, results of operations in the network and thus system functioning results and the functioning alternations are characterized by random values. To systematize possible states during the network of operations, we propose a new type of graph-theoretic model-a Complex State-Transition Tree of Action Networks. Each node of the tree corresponds to the system's state, and each branch to the possible system state transition and both may take complex form (Hypergraph of states and Network of actions respectively). Each possible workplace state corresponds to the possible operation or waiting for the operation's realization at this workplace. Thus, the states of the tree of possible states corresponds to the network of actions (operations') possible cuts. To create trees of possible states mappings to the networks of actions cuts, an algorithm to build such trees from networks of operations is suggested. It differs from a known algorithm of maximum network flow in that all possible cuts of the network and all possible states are modelled. It differs from a known algorithm of building all antichains of the partially ordered set (poset) in that the network of operations we consider may not constitute such poset.