Given a TM M, does M enter every non-halting state when run on a blank tape? Is there an input that causes M to enter every non-halting state?

  1. $ L=\{M\enspace|\enspace \text{M is a TM that enters every non-halting state starting with a blank tape} \}$
    My professor proved this language undecidable by taking a generic TM and rerouting the states that go to a halt state to pass by every other state (and a new flag state) before halting.
    So now if I had a decider for $ L$ I could decide Halting because the modified machine halts if the decider returns 1 or doesn’t halt if it returns 0.

    Now my question is: can i simplify the proof by just creating a machine $ N$ with just one non-halting state (the inital state $ q_0$ ) that accepts everything, then use Rice’s theorem:

    • take an instance of Halting $ (M,w)$
    • create a machine $ N’$ that starts the machine $ N$ with input $ \epsilon$ only if $ M$ halts on $ w$ and returns the output of $ N$
      So $ N$ and $ N’$ will look like this:
      machines N and N'
      Now if $ M$ halts on input $ w \implies N’$ halts on input $ \epsilon$ (blank tape) $ \implies N’\in L$ since it only has the starting state as non-halting state;
      if $ M$ does not halt on input $ w \implies N’$ does not start $ \implies N’\notin L$ since it doesn’t visit any of its states.

      On the other hand if $ N’\in L \implies M$ halted with input $ w$ (otherwise $ N$ wouldn’t have started and it wouldn’t have visited any state);
      if $ N’\notin L\implies M$ did not halt on input $ w$ (otherwise $ N$ would have started and visited its only non-halting state).

      Since $ M(w)$ halts $ \iff N’\in L$ and $ M(w)$ does not halt $ \iff N’\notin L$ , having a decider for $ L$ would decide the Halting problem.
      Is this proof correct?

  2. $ L=\{M\enspace|\enspace \text{M is a TM and there exists an input s.t. M enters every non-halting state} \}$
    This I have to say if it’s decidable or undecidable.
    I’m thinking undecidable because if I take the modified machine of the previous proof (the one that visits every state iff it halts), call it $ P$ , and take the complement of $ L$ , i.e. $ L’=\{M\enspace|\enspace \text{M is a TM s.t. there exists no input s.t. M enters every non-halting state} \}$
    then $ P\in L’\iff$ there exists no input that makes $ P$ halt, i.e. $ P$ accepts nothing. Since $ P$ is the mod of a generic machine, having a decider for $ L’$ would decide AcceptsNothing problem that we know is undecidable.
    Now since $ L’$ is not decidable neither can be $ L$ .
    Is this correct?

Enter key intermittently stops working on both my Macbook Pro’s & external keyboard

My Macbook Pro is 5 months old and I’ve started to get “enter” key failure on both my internal and external keyboards. It works again when I restart the laptop. The fact that it’s happening on both keyboards tells me that it’s not a hardware issue per say. I’ve cleaned both keyboards to make sure it wasn’t due to a dirty underside of the keys. Can anyone provide some guidance on this?

How do I enter disk location on Ubuntu 18 in Nautilus / Files?

I switched from ubuntu 14 to ubuntu 18 and I am puzzled big time how to do simple functions:

For example on ubuntu 14 I had chance to open dialog and enter disk path. I have no idea how to do this with new Ubuntu/Nautilus.

I have Ubuntu 18.04.1 and Files 3.26.4 …

How it looks to me Nautilus got cut from left to right and from up to down. I cannot find a lot of functions that I was able to do earlier. Some things are made really user friendly and to some degree better but at some points being unable to do things gets really annoying to the point that I think of going back to previous version of OS.

How do I enter disk location on Ubuntu 18 in Nautilus / Files?

I switched from ubuntu 14 to ubuntu 18 and I am puzzled big time how to do simple functions:

For example on ubuntu 14 I had chance to open dialog and enter disk path. I have no idea how to do this with new Ubuntu/Nautilus.

I have Ubuntu 18.04.1 and Files 3.26.4 …

How it looks to me Nautilus got cut from left to right and from up to down. I cannot find a lot of functions that I was able to do earlier. Some things are made really user friendly and to some degree better but at some points being unable to do things gets really annoying to the point that I think of going back to previous version of OS.

Enter Australia on an expired passport

I am a dual citizen Australian / British. I have let my Australian passport expire, however due to a change in circumstances in the UK I am looking to return to Australia permanently within the next couple of weeks.

Will I be able to: a) board a flight out of the UK on a one-way ticket? b) be allowed to re-enter Australia with my expired passport

Thanks in advance.

a

Automator and/or AppleScript to automatically Command-F2 to enter Target Display Mode

I’m trying to use Automator with AppleScript to automatically hit Command + F2 to enter Target Display Mode. The script runs but I just get a beep/tone with no action. I don’t know if there’s an error in the script or if it’s not capable of hitting a function key.

on run {input, parameters}      tell application "System Events"         key down {command}         keystroke "120"         key up {command}     end tell return input end run 

Once I get this working I’ll need to somehow schedule this to run on startup or maybe on a schedule. I’ve seen some threads on this but never an actual solution. I’m using a 2011 iMac as a secondary monitor and hate hitting Command + F2 every day.

Can i enter UK for 24 hours from a schengen area holding an indian passport?

I am travelling to Poland and Netherlands , flying on 25th June holding a schengen business visa. For the weekend , can i plan to go to UK(just sunday). Not planning to stay overnight. 1 day return trip. I hold an indian passport (No USA visa stamped). Can i get a transit visa for 24 hours with this? Please help.

Can’t enter directory despite correct permissions

I have a directory (Owned by nobody due to it being a part of a Docker bind mount, combined with user namespace remapping.) that I need to enter. This is its relevant ls -la output:

drwxrwxr-x    2 nobody   nobody        4096 May 26 14:42 Directory 

Running as root, although I don’t belong in either the owner or group of the directory, the directory is world readable and executable, so I should be able to enter it. However, when running cd Directory, it fails:

bash: cd: Directory: Permission denied