1. (Exercise 4.4) Let AεCFG = {<G> | G is a CFG that generates ε}. Show that AεCFG is decidable.
2. Consider the problem of determining if a DFA accepts any string of length 3. Formulate this problem as a language and show that it is decidable.
3. Consider the following language L1.
L1 = {< M,w > | M is a TM and input w causes M to move its
head to the blank portion of the tape}.
Show that L1 is decidable.
4. Consider the following language L2.
L2 = {< M,w,q > | M is a TM, q is a state, and M enters
state q during the computation on w}.
Use reduction to show that L2 is undecidable.
5. Consider the problem of determining if a Turing machine
rejects at least two strings, i.e., rejects two or more strings.
Formulate this problem as a
language and show that it is undecidable.