On the Structure of Logspace Probabilistic Complexity Classes

Ioan I. Macarie
2000 SIAM journal on computing (Print)  
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 veri ers. For each log-space complexity class, we decompose it into a hierarchy based on corresponding multihead two-way nite 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
more » ... omplexity class to low levels of its corresponding hierarchy. We nd 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 nite automata with probabilistic (probabilistic and nondeterministic) states.
doi:10.1137/s0097539796298339 fatcat:rmejwvw7irbpllyy4f57yvkffa