I have a finite automaton with these properties:Contains cyclesIt's a directed graphAll the states/nodes are initialy reachable from the initial stateIt has final states but I guess it isn't relevant for my issueIt's a random generated automaton, and the generation isn't meant to satisfy properties like strongly connected components or connected components Let's suppose I have to delete an edge. I need to know if there's a way to prove that the reached state by this edge is still reachable from the initial state without using a classical search (DFS or BFS); obviously, if there is any.
What is the optimal solution to prove the reachbility of a node from the root?
graph theory;finite automata;graph traversal