55 citations · 60 across the 5 of their papers we have counts for
5 papers
Using biased coins as oracles
Toby Ord, Tien D. Kieu
While it is well known that a Turing machine equipped with the ability to flip a fair coin cannot compute more that a standard Turing machine, we show that this is not true for a b…
The Diagonal Method and Hypercomputation
Toby Ord, Tien D. Kieu
The diagonal method is often used to show that Turing machines cannot solve their own halting problem. There have been several recent attempts to show that this method also exposes…
Representations of Omega in Number Theory: Finitude Versus Parity
Toby Ord, Tien D. Kieu
We present a new method for expressing Chaitin's random real, Omega, through Diophantine equations. Where Chaitin's method causes a particular quantity to express the bits of Omega…
On the existence of a new family of Diophantine equations for
Toby Ord, Tien D. Kieu
We show how to determine the -th bit of Chaitin's algorithmically random real number by solving instances of the halting problem. From this we then reduce the problem of…
Hypercomputation: computing more than the Turing machine
Toby Ord
Due to common misconceptions about the Church-Turing thesis, it has been widely assumed that the Turing machine provides an upper bound on what is computable. This is not so. The n…