CSE 355 Quiz 12
Under what operations are recognizable languages not closed?(a) Complement. (b) Union. (c) Intersection. (d) Star. (e) Recognizable languages are closed under all of these operations.
A
Consider the problem of determining, from a given PDA, whether the PDA has infinite language or not. Is this decidable or not? And why or why not? (a) Decidable: because from class we saw that we can detect looping conditions and just delete them if there are any (and say that it is infinite if there are such conditions). (b) Decidable: because of the pumping lemma for CFLs. (c) Undecidable: one would need to keep track of infinitely many strings that are accepted by the PDA (through simulation). (d) Undecidable: if one can decide this problem, then one can decide the acceptance problem for TMs, which we already know is undecidable. (e) None of the above is correct.
B
My friend is curious about the language: L = {<M> : M is a TM and accepts at least 3 strings}. Is this language decidable? Why or why not? (a) Decidable: test strings until 3 are found to be accepted by the machine. (b) Decidable: the machine's language must be finite, and therefore decidable. (c) Undecidable: we can construct a decider for ATM assuming a decider for this language. (d) Undecidable: we can construct a decider for this language assuming a decider for ATM. (e) None of the above is true.
C
Anaconda Corporation has announced a new product that, when given a Python program P as input, can determine whether P can go into an infinite loop on any input. Which of the following is true? (a) Anaconda Corporation is scamming me because they are snakes. (b) Their product might work because it only handles Python programs. (c) Their product might work if it has a library of every possible Python program. (d) Their product does not work because Turing machines can be converted to Python programs. (e) Their product does not work because Python programs can be converted to Turing machines.
D
My friend does not believe the fact that A_TM is undecidable because he says that he can tell whether his program is in an infinite loop on a given input. Suppose that my friend has a specific program M and a specific input w. He defines the language L = {0} if M halts on input w and L = {1} if M goes into an infinite loop on input w. Then L is: (a) Undecidable because A_TM is undecidable (b) Undecidable because if M goes into an infinite loop we can never be sure that it is in one (c) Decidable because my friend says so (d) Decidable because L is regular (e) Perhaps decidable and perhaps undecidable, depending on what M and w are.
D
SUB_PDA = {<M1, M2> | M1, M2 are PDAs and L(M1) ⊆ L(M2)} is decidable.
False
The problem of whether a given TM has at least 355 strings in its language or not is decidable.
False
There is an enumerator that has a language that is not recognizable.
False
FINITE_DFA = {<M> | M is a DFA with finite language} is decidable.
True
There is a recognizer that has an undecidable language.
True
