Abstract
Abstract Adapting a method that Freivalds used in the context of bounded-error probabilistic computation, we prove that the languages recognized by log-space un bounded-error probabilistic Turing machines (PL) are log-space reducible to languages recognized by automata of the same type but restricted to use at most e log n bits of storage space, for arbitrarily small e s 0. Furthermore, we show that the banded-matrix inversion problem Band-Mat-Inv( n e ) is log-space complete for PL, for any e ϵ (0, 1]. This strengthens a result of Jung that Band-Mat-Inv( n ) is log-space complete for PL, and may lead to new space-efficient deterministic simulations of space-bounded probabilistic Turing machines.
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