William Umboh
banner
swumboh.bsky.social
William Umboh
@swumboh.bsky.social
Lecturer in Computational Theory, School of Computing and Information Systems, University of Melbourne. Interests: Theoretical computer science and combinatorial optimisation, focussing on approximation and online algorithms. williamumboh.com
Hoping they release a tldr version called Sublinear Times.
November 26, 2025 at 3:22 AM
One positive aspect is that it’s easier to see the proof as an algorithm. So i ask them to code it up and the tests give them feedback as to whether they understand the format of the proof. It also makes it much easier to scaffold for them.

I wrote up some notes at williamumboh.com/comp30026-20...
Proving Nonregularity - Models of Computation
williamumboh.com
November 15, 2025 at 11:12 AM
Yeah, we are marking the exams now. I think it went really well! I went with fooling sets instead of pumping lemma to prove non regularity. Feedback from the tutors and students have been positive.
November 15, 2025 at 11:12 AM
Ah ok, good point, thanks!

The usual diagonalization proof avoids the encoding issue as it constructs a machine D that on input <M> runs H on <M>, <M> and does the opposite.
November 8, 2025 at 9:48 AM
Clearly, L cannot exist since it accepts w iff it rejects w. QED.

Does this work?
November 8, 2025 at 7:28 AM
Suppose, towards a contradiction, that there is a machine H that can decide if any given Turing machine M accepts any given input string w.

Consider the following machine L:

On input w:
Run H to see if L accepts w
Accept if H rejects
Reject if H accepts
November 8, 2025 at 7:28 AM
Wow, outsold monopoly! youtu.be/Hxn0NUbIVbo?...
TODAY SHOW meets A GAME CALLED BIRDS
YouTube video by agamecalledbirds
youtu.be
October 26, 2025 at 6:14 AM
I spend way too much time grep-pling text files as well
October 26, 2025 at 4:21 AM
launch party when?
October 25, 2025 at 2:37 AM
English is an unpossible language
October 9, 2025 at 11:28 AM