A language is undecidable if there is no Turing Machine that will recognize that language and halt on all inputs. Show that the following language is undecidable: A = {M | M is a Turing machine that accepts exactly all the odd length strings} The intended solution is to reduce from the halting problem, which we will show is undecidable. The halting problem is given a Turing machine M and an input w, decide whether M terminates when given w as input

A is undecidable

Explanation:

construct aTM TI that will accept on input x |X| is odd if |X| is even, it stimulates M on input w.

TI enters the reject state when M accept w. when M rejects w, T1 enters accept state.

Observe that if M accept W, then t1 is a turning machine that accepts all inputs of odds length. If M rejects or loops on input w, then T1 is a turning machine that rejects the loop.

maybe when you are listing people names in a job.

i am not 100% sure

given the lack of choices, i'm gonna wing it and say that pushing your car off a cliff might not be the best idea. your car might sustain damage from the fall and will probably result in the car being too damaged to jump start.

if that's not good enough, avoid filling the car with bees. bees might get agitated when trapped or during the moving process, and might result in death or painful stings that will make jump starting your car very difficult. but in the event that you do choose to fill your car with bees, remember to wear protective gear!