Automata system: composition according to graph of links

The problem of modeling and composing of aggregate systems is considered. The system components are described with finite automata with multiple entries and exits. The communication between automata is described with message passing over simplex communication channels. The system is described with a directed graph of links. Each node of the graph corresponds to automaton of a component and an arc corresponds to a communication channel connecting exit of one automaton with entry of another automaton. Automaton of the graph node in each state can accept multiple messages from its entries (at most one message from each entry) and send multiple messages to its exits (at most one message to each exit). Entries (exits) of the automata not connected to exits (entries) of automata are considered to be external and used for communication between the system and its environment. The automata of the system operate synchronously: on each cycle each automaton performs one transition. A transition of an automaton imposes requirements on states of all its entries and exits (messages in them are specified) and explicitly specifies subset of entries and exits through which the messages are received or sent, respectively. Synchronous communication between automata means that for each link the requirements of the automata connected with this link must conform to each other. It makes possible to describe a wider spectrum of automata behavior. For example, a priority of message receiving: if there are multiple message in the automata entries, it can receive messages with the highest priority and discard the rest of the messages. It also makes possible for the automaton to receive messages regardless of ability to simultaneously send some message to some exit. A composition of the automata of the system according to the graph of links is defined and its associativity is proved. In conclusion, the directions of future research are described.