## Reproducibility and pseudo-determinism in log-space

##### Author(s)

Grossman, Ofer.
Download1192476024-MIT.pdf (748.4Kb)

##### Other Contributors

Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science.

##### Advisor

Shafi Goldwasser.

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Show full item record##### Abstract

A curious property of randomized log-space search algorithms is that their outputs are often longer than their workspace. This leads to the question: how can we reproduce the results of a randomized log space computation without storing the output or randomness verbatim? Running the algorithm again with new random bits may result in a new (and potentially different) output. We show that every problem in search-RL has a randomized log-space algorithm where the output can be reproduced. Specifically, we show that for every problem in search-RL, there are a pair of log-space randomized algorithms A and B where for every input x, A will output some string t[subscript x] of size O(log n), such that B when running on (x, t[subscript x]) will be pseudo-deterministic: that is, running B multiple times on the same input (x, t[subscript x]) will result in the same output on all executions with high probability. Thus, by storing only O(log n) bits in memory, it is possible to reproduce the output of a randomized log-space algorithm. An algorithm is reproducible without storing any bits in memory (i.e., lt[subscript x]l = 0) if and only if it is pseudo-deterministic. We show pseudo-deterministic algorithms for finding paths in undirected graphs and Eulerian graphs using logarithmic space. Our algorithms are substantially faster than the best known deterministic algorithms for finding paths in such graphs in log-space. The algorithm for search-RL has the additional property that its output, when viewed as a random variable depending on the randomness used by the algorithm, has entropy O(log n).

##### Description

Thesis: S.M., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, May, 2020 Cataloged from the official PDF of thesis. Includes bibliographical references (pages 31-33).

##### Date issued

2020##### Department

Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science##### Publisher

Massachusetts Institute of Technology

##### Keywords

Electrical Engineering and Computer Science.