# Deterministic simulation in LOGSPACE

@article{Ajtai1987DeterministicSI, title={Deterministic simulation in LOGSPACE}, author={Mikl{\'o}s Ajtai and John Komlos and Endre Szemer{\'e}di}, journal={Proceedings of the nineteenth annual ACM symposium on Theory of computing}, year={1987} }

In this paper we show that a wide class of probabilistic algorithms can be simulated by deterministic algorithms. Namely if there is a test in LOGSPACE so that a random sequence of length (log n)2 / log log n passes the test with probability at least 1/n then a deterministic sequence can be constructed in LOGSPACE which also passes the test. It is important that the machine performing the test gets each bit of the sequence only once. The theorem remains valid if both the test and the machine…

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