The Turing degree of a real number x is defined as the Turing degree of its binary expansion. This definition is quite natural and robust. In this paper we discuss some basic degr...
In this paper we study quantum computation from a complexity theoretic viewpoint. Our first result is the existence of an efficient universal quantum Turing machine in Deutsch’s...
Maurer machines are much closer to real computers than Turing machines. Computer instructions play a prominent part in Maurer machines. We show a straightforward way to simulate Tu...
The intuition guiding the de…nition of computation has shifted over time, a process that is re‡ected in the changing formulations of the Church-Turing thesis. The theory of co...
We give small universal Turing machines with state-symbol pairs of (6, 2), (3, 3) and (2, 4). These machines are weakly universal, which means that they have an infinitely repeate...