Computational Limitations of Stochastic Turing Machines and Arthur-Merlin Games with Small Space Bounds

@inproceedings{Liskiewicz1997ComputationalLO,
  title={Computational Limitations of Stochastic Turing Machines and Arthur-Merlin Games with Small Space Bounds},
  author={Maciej Liskiewicz and R{\"u}diger Reischuk},
  booktitle={MFCS},
  year={1997}
}
A Stochastic Turing machine (STM) is a Turing machine that can perform nondeterministic and probabilistic moves and alternate between both types. Such devices are also called games against nature, Arthur-Merlin games, or interactive proof systems with public coins. We give an overview on complexity classes defined by STMs with space resources between constant and logarithmic size and constant or sublinear bounds on the number of alternations. New lower space bounds are shown for a specific… 
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On small space complexity classes of stochastic Turing machines and Arthur-Merlin-games
TLDR
This work investigates stochastic machines with space resources between constant and logarithmic size, and constant or sublinear bounds on the number of alternations between nondeterministic and probabilistic moves, and nonclosure properties of certain classes.
Probabilistic Algorithms and Complexity Classes
TLDR
This dissertation considers the computation which will always terminates in bounded time, as opposed to expected time, and shows that the coin with probability 1 2 or 1 3 is more expressive coin than the others, and designs an NC approximation algorithm for a variation of the shortest superstring problem.
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