Space and time complexity for infinite time Turing machines

Space Complexity in Infinite Time Turing Machines

Infinite-Time Turing Machines and Borel Reducibility

In this document I will outline a couple of recent developments, due to Joel Hamkins, Philip Welch and myself, in the theory of infinite-time Turing machines. These results were obtained with the idea of extending the scope of the study of Borel equivalence relations, an area of descriptive set theory. I will introduce the most basic aspects of Borel equivalence relations, and show how infinite...

Cardinal-Recognizing Infinite Time Turing Machines

We introduce a model of infinitary computation which enhances the infinite time Turing machine model slightly but in a natural way by giving the machines the capability of detecting cardinal stages of computation. The computational strength with respect to ITTMs is determined to be precisely that of the strong halting problem and the nature of the new characteristic ordinals (clockable, writabl...

Zeno machines and Running Turing machine for infinite time

This paper explores and clarifies several issues surrounding Zeno machines and the issue of running a Turing machine for infinite time. Without a minimum hypothetical bound on physical conditions, any magical machine can be created, and therefore, a thesis on the bound is formulated. This paper then proves that the halting problem algorithm for every Turing-recognizable program and every input ...

Verifying time complexity of Turing machines

We show that, for all reasonable functions T (n) = o(n log n), we can algorithmically verify whether a given one-tape Turing machine runs in time at most T (n). This is a tight bound on the order of growth for the function T because we prove that, for T (n) ≥ (n+1) and T (n) = Ω(n log n), there exists no algorithm that would verify whether a given one-tape Turing machine runs in time at most T ...