I know this is a bit pedantic but I'm curious of the definition of finite automata. In Theory of Computation Sipser states
The formal definition says that a finite automaton is a list of those five objects: set of states, input alphabet, rules for moving, start state, and accept states.
I've seen definitions where "input alphabet" is replaced by "input language". Which is right? Isn't it more right to say "language" as a machine recognizes the strings that make up the language, not the individual symbols that make up the alphabet?