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Deterministic simulation in LOGSPACE

Authors:

M. Ajtai,

J. Komlos,

E. SzemerediAuthors Info & Claims

STOC '87: Proceedings of the nineteenth annual ACM symposium on Theory of computing

Pages 132 - 140

https://doi.org/10.1145/28395.28410

Published: 01 January 1987 Publication History

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Abstract

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 constructing the satisfying sequence have access to the same oracle of polynomial size.

The sequence that we construct does not really depend on the test, in the sense that a polynomial family of sequences is constructed so that at least one of them passes any test. This family is the same even if the test is allowed to use an oracle of polynomial size, and it can be constructed in LOGSPACE (without using an oracle).

References

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M. Ajtai and A. Wigderson. "Deterministic simulation of probabilistic const~tnt depth circuits", iBM Research Report, RJ 4866 (51296) 10/3/85 or FOCS, 1985, pp 11-19

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Deterministic simulation in LOGSPACE

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STOC '87: Proceedings of the nineteenth annual ACM symposium on Theory of computing

January 1987

471 pages

ISBN:0897912217

DOI:10.1145/28395

Editor:
Alfred V. Aho

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 01 January 1987

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STOC87: 19th Annual ACM Conference on Theory of Computing

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https://dl.acm.org/doi/10.4230/LIPIcs.CCC.2023.8
Cohen GMaor GSaha BServedio R(2023)Random Walks on Rotating ExpandersProceedings of the 55th Annual ACM Symposium on Theory of Computing10.1145/3564246.3585133(971-984)Online publication date: 2-Jun-2023
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Logspace Optimization Problems and Their Approximability Properties

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Logspace Optimization Problems and Their Approximability Properties

Canonizing Graphs of Bounded Tree Width in Logspace

Logspace optimization problems and their approximability properties

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