Abstract
We investigate hierarchies of complexity classes defined by log-space probabilistic Turing machines, Arthur-Merlin games and Games against nature with logarithmic space-bounded probabilistic verifiers. We decompose each log-space complexity class into a hierarchy based on corresponding multihead two-way finite-state automata and we prove the separation of the levels of several hierarchies even over a one letter alphabet; furthermore, we show deterministic log-space reductions of each log-space complexity class to low levels of its corresponding hierarchy.
We find probabilistic (and “probabilistic+nondeterministic”) variants of Savitch's maze threading problem that are log-space complete for PL (and respectively P) and that can be recognized by two-head one-way and one-head one-way one-counter finite-state automata with probabilistic (probabilistic and nondeterministic) states.
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Macarie, I.I. (1995). On the structure of log-space probabilistic complexity classes. In: Mayr, E.W., Puech, C. (eds) STACS 95. STACS 1995. Lecture Notes in Computer Science, vol 900. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-59042-0_107
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DOI: https://doi.org/10.1007/3-540-59042-0_107
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