Abstract
Recent research in theoretical physics on ‘Malament-Hogarth space-times’ indicates that so-called relativistic computers can be con- ceived that can carry out certain classically undecidable queries in fi- nite time. We observe that the relativistic Turing machines which model these computations recognize precisely the Δ2-sets of the Arithmetical Hierarchy. In a complexity-theoretic analysis, we show that the (infinite) computations of S(n)-space bounded relativistic Turing machines are equivalent to (finite) computations of Turing machines that use a S(n)- bounded advice f, where f itself is computable by a S(n)-space bounded relativistic Turing machine. This bounds the power of polynomial-space bounded relativistic Turing machines by TM/poly. We also show that S(n)-space bounded relativistic Turing machines can be limited to one or two relativistic phases of computing.
This research was partially supported by GA ČR grant No. 201/02/1456 and by EC Contract IST-1999-14186 (Project ALCOM-FT).
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Wiedermann, J., van Leeuwen, J. (2002). Relativistic Computers and Non-uniform Complexity Theory. In: Unconventional Models of Computation. UMC 2002. Lecture Notes in Computer Science, vol 2509. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45833-6_24
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DOI: https://doi.org/10.1007/3-540-45833-6_24
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