This is a question concerning Kripke automaton. My answers seem a little short and I was wondering if I was missing something?Transition table of a Kripke automaton: A -> red light is onB and D -> blue light is onC -> both light are on1) Is the test 001blue satisfied by any state?Attempt: No2) Is the test 001red satisfied by every state?Attempt: Yes but I dont know how to show it.3) Which test could tell difference btw A and C?Attempt: test = 100both; C satisfies test, A doesnt4) Can any test distinguish B and C?Attempt: Yes, test = 10001blue; B satisfies test, C doesnt5)Show that no test can tell the difference btw B and D.Attempt: Their observations are different.
Kripke automaton and observations
automata
Your answers seem correct.As for 2: one way is to simply check, a quicker way is to observe that all states go to A upon reading 1, so the sequence 001 ends in A, and A satisfies red.3 can be solved by the test blue (without any moves) and 4 can be solved with the test red.As for 5: in order to show that no test can differentiate B and D, observe that for the letter 1, both go to A, for the letter 0 both go to C, and both have the same light (blue). Thus, you can say that the language of both state is equal.