18,014 research outputs found
On Halting Process of Quantum Turing Machine
We prove that there is no algorithm to tell whether an arbitrarily
constructed Quantum Turing Machine has same time steps for different branches
of computation. We, hence, can not avoid the notion of halting to be
probabilistic in Quantum Turing Machine. Our result suggests that halting
scheme of Quantum Turing Machine and quantum complexity theory based upon the
existing halting scheme sholud be reexamined.Comment: 2 page
Verifying Time Complexity of Deterministic Turing Machines
We show that, for all reasonable functions , we can
algorithmically verify whether a given one-tape Turing machine runs in time at
most . This is a tight bound on the order of growth for the function
because we prove that, for and , there
exists no algorithm that would verify whether a given one-tape Turing machine
runs in time at most .
We give results also for the case of multi-tape Turing machines. We show that
we can verify whether a given multi-tape Turing machine runs in time at most
iff for some .
We prove a very general undecidability result stating that, for any class of
functions that contains arbitrary large constants, we cannot
verify whether a given Turing machine runs in time for some
. In particular, we cannot verify whether a Turing machine
runs in constant, polynomial or exponential time.Comment: 18 pages, 1 figur
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