Introduction
In the existing literature on infinite time Turing machines (ITTM), which were originally defined in [3], issues of time complexity have been widely considered. The question \(\mathbf{P} \stackrel{?}{=} \mathbf{NP}\) for Infinite Time Turing Machines, and several variants on it, are treated in, e.g., [6],[2], and [4].
Besides time complexity, we may also try to look at issues of space complexity in ITTMs. However, because an ITTM contains tapes of length ω, and all nontrivial ITTM computations will use the entire, ω-length tape, simply measuring the space complexity by counting the portion of the tape used by the computation is not an option. In [5], therefore, an alternate notion of space complexity is provided, that is based on looking at the levels of Gödel’s constructible hierarchy where the snapshots of the computation can be found.
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Winter, J. (2009). Is P = PSPACE for Infinite Time Turing Machines?. In: Archibald, M., Brattka, V., Goranko, V., Löwe, B. (eds) Infinity in Logic and Computation. ILC 2007. Lecture Notes in Computer Science(), vol 5489. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03092-5_10
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