Abstract
A probabilistic Turing machine (PTM) is a Turing machine that flips an unbiased coin to decide its next movement and solves a problem with some error probability. It is expected that PTMs need more time if a smaller error probability is required. This is a sort of time-precision tradeoff and is shown to occur actually on on-line probabilistic Turing machine acceptors (ONPTMs). That is, we show the existence of a set such that it is recognized by an ONPTM with 1 2 -( logn)/ 8n bounded error probability in O( n) time but for every ε, 0<ε< 1 2 , it requires more than O(( n/log n) 2) time to recognize this set with bounded error probability by ONPTMs. Moreover our result is also shown to be an example of difference between nondeterministic computations and probabilistic ones.
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