On the Power of Randomized Pushdown Automata
DLT '01 Revised Papers from the 5th International Conference on Developments in Language Theory
On the power of randomized multicounter machines
Theoretical Computer Science - Insightful theory
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We investigate hierarchical properties and log-space reductions of languages recognized by log-space probabilistic Turing machines, Arthur-Merlin games, and Games against Nature with log-space probabilistic verifiers. For each log-space complexity class, we decompose it into a hierarchy based on corresponding multihead two-way finite automata and we (eventually) prove the separation of the hierarchy levels (even over one letter alphabet); furthermore, we show log-space reductions of each log-space complexity class to low levels of its corresponding hierarchy. .pp We find probabilistic (and ``probabilistic+nondeterministic'''') variants of Savitch''s maze threading problem which are log-space complete for PL (and respectively P) and can be recognized by two-head one-way and one-way one-counter finite automata with probabilistic (probabilistic and nondeterministic) states.