BLUF: This repo demonstrates the reduction pattern in runnable form under explicit bounds. It does not solve the Halting Problem, and it is not a safety certification tool for real autonomous systems.

Abstract: The purpose of this paper is to gain a better understanding of the structure of undecidable problems in automata theory by investigating the degree of unsolvability of these problems. This ...

Abstract: In this paper, we propose several opacity-preserving (bi)simulation relations for nondeterministic transition systems (NTSs) in terms of initial-state opacity, current-state opacity, K-step ...

The original version of this story appeared in Quanta Magazine. The world of mathematics is full of unreachable corners, where unsolvable problems live. Now, yet another has been exposed. In 1900, the ...

The French scholar Pierre-Simon Laplace crisply articulated his expectation that the universe was fully knowable in 1814, asserting that a sufficiently clever “demon” could predict the entire future ...

The problems in the library can mostly be categorized into seed problems, advanced problems, and target problems. Seed problems are simple to state and thus make for good starting points of ...

Katie has a PhD in maths, specializing in the intersection of dynamical systems and number theory. She reports on topics from maths and history to society and animals. Katie has a PhD in maths, ...

Ask the publishers to restore access to 500,000+ books. An icon used to represent a menu that can be toggled by interacting with this icon. A line drawing of the Internet Archive headquarters building ...

Moral dilemmas are often undecidable. Which is to say, there are times when we lack solid rational grounds for choosing between two (or more) compelling courses of action. In those moments, after ...

Things equal to the same thing are also equal to one another. And if equal things are added to equal things then the wholes are equal. And if equal things are subtracted from equal things then the ...

Aug 2: I'll have 2-hour office hours on Wed, Aug 7, 11:30-13:30. Aug 2: The final exam on Aug 8 will be on all topics of the course, with equal emphasis. You'll have 3 hours for an exam that will be ...