Converting DFA to Regular Expression Using State Removal

I’m trying to convert the following NFA to a regular expression.

I’ve attached my work below and end up with the expression $ aa^*bb^*$ . As far as I can tell, this doesn’t seem correct but I’ve been working at it for quite a while. Can anyone tell me where I went wrong? And if it happens to be correct, can you tell me why?

Thanks a lot in advance.


Upon further work, I came up with the regular expression: $ aa^*b(b\cup aaa^*b)^*$ . This seems like the correct response.

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ProPDFConverter virus removal help

So, I foolishley managed to get my computer infected with a browser hijacker called ProPDFConverter, which

devious web site or extension that has big resemblance to legitimate search engine based on appearance. It quietly enters into the computer and swiftly alters your default home page and new tab. All of a sudden, your main search application will be replaced with ProPDFConverter.

Indeed, whenever I opened a new tab it lead me to this obviously malicious search engine. When I first relized what happened, I immidiatly just removed the extention – which had the same name as the virus – from my Google Chrome, and on the surface, it helped: from this moment on, my browser got back to normal. But just to be sure, I searched for some information about this virus, and ran into some removal guides for it. All of them, without exeption, suggested to do the extention-removal bit LAST, after running malware scans and uninstall the program through the control panel.

And this is where the problem hit: I ran TWO different virus/malware scans, one with MalwareBytes and one with Norton Power Eraser, and both resulted in “no threats found”. When accessing the “uninstall a program” option in the control panel, I also could not locate a program with a simillar name to that of virus/extention. Infact, I could not locate any new programs from the date of the infection (October 9th). Both these facts seem very very odd.

So by all accounts, it seems that I solved the problem by just removing the exention from chrome, but I don’t know, it seems WAY TOO EASY to be true. I’m afraid that there are still some dangerous remenants of the virus of my PC, and neither I or any security program manages to locate them.

Am I just overlly paranoid, or is are there still remenants of the virus on my computer after all? If yes, How can I find out and remove them? And does this virus even does anything else other than that browser hajacking which I seemingly fixed?

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Algorithm to solve a physical ring removal puzzle

Assume we want to solve the so-called “Super-G” problem from Jean-Claude Constantin. The goal of the puzzle is to get the ring off the other components. Here is a picture of the problem:

Picture of Super-G problem Source:

The question here shall not be how to do that – that’s trivial after you figured out. The question shall be, how we can write a simulation for this problem that seeks for the proper solution.

I can think of two completely different approaches, both of them non-trivial:

  • May we find a way to represent all moves that we can do in an abstract way? The simulation would be trivial.
  • Should we use a 3D simulation and use some random walk to move the ring? The set-up might be much simpler, but the simulation itself much harder, also because the line might be very hard to simulate.

We are not looking for a solution in the form of a code, but what approach should be taken.

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