Graph learning by interacting automata

The paper describes the learning an unknown oriented graph by automata traversing the arcs of the graph and exchanging messages. The learning completes when each arc has been traversed by at least one automaton. Section 1 discusses the problems of identification of arcs and nodes in the graph, ways of exchanging messages between automata and interaction of the automata with the graph. The arcs outgoing from the same node are considered enumerated. When traversing the graph, each automaton indicates the number of the arc outgoing from the current node. The nodes have unique identifiers. The exceptions are sinks and nodes with only one incoming arc: these nodes can have empty identifier. Automaton can recognize the identifier of the current node and the number of outgoing arcs. The automata interaction media provides message transfer from one automaton to another in a limited time. The following primitives are recognized: "send message"indicating the receiver address and "receive message from any sender". Section 2 describes the idea of the algorithm. Automata are divided into regulators and runners. Runners traverse the arcs of the graph. When in a new (yet untraversed) node, runner becomes its regulator. The node regulator controls the runners travel along the arcs outgoing from this node. The regulator of the initial node, in addition, generates new runners. During execution, the graph description is created in the cumulative memory of the regulators as a spanning tree of the already traversed part of the graph oriented form the initial node. To navigate the runners, the following message is used: "where to"from runner to regulator and response message "traverse the arc"indicating the arc number and the address of the regulator of the arc terminal node if this arc has already been traversed. Regulator sends runners either along the arcs of the tree or along untraversed arcs. After traversing an untraversed arc, runners learn the identifier of its terminal node, but it needs to know whether this node has been already traversed. To get this information, the "poll" message is sent iterating all regulators linked into a list of addresses. If the node has been traversed, the node regulator sends the response message to the runner indicating its address, and the runner resends this address to the regulator of the initial node of the traversed chord in the "finish"message. This message is also used to indicate the traversal end: the regulator of the tree arc terminal node sends "finish"to the regulator of the arc initial node if it has received "finish"along all outgoing arcs. The traversal is over when regulator of the initial node receives "finish"along all outgoing arcs. Section 3 gives the estimate of the traversal time. (m+ nD), where n is a number of nodes, m is a number of arcs, and D is the maximal number of nodes with nonempty identifiers on the graph path from the initial node. The conclusion describes possible directions of further work: learning of nondeterministic graphs, use of external memory, learning graphs of special kind.