Decide whether a DFA accepts at least two strings Is the following language decidable? $$L = \{A : \text{A is a DFA and } |L(A)| \ge 2\}$$
First remove dead states(those which do not lead to accept states). Then run depth first search. If all accepts states are not reachable or there is a single path leading to an accept state then REJECT. If there are two different paths leading to an accept state (or accept states) then ACCEPT. If there is a cycle including a state from which an accept is reachable also ACCEPT.