Derandomization with Minimal Memory Footprint

Dean Doron, Roei Tell

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Existing proofs that deduce BPL = L from circuit lower bounds convert randomized algorithms into deterministic algorithms with large constant overhead in space. We study space-bounded derandomization with minimal footprint, and ask what is the minimal possible space overhead for derandomization. We show that BPSPACE[S] ⊆ DSPACE[c·S] for c ≈ 2, assuming space-efficient cryptographic PRGs, and, either: (1) lower bounds against bounded-space algorithms with advice, or: (2) lower bounds against certain uniform compression algorithms. Under additional assumptions regarding the power of catalytic computation, in a new setting of parameters that was not studied before, we are even able to get c ≈ 1. Our results are constructive: Given a candidate hard function (and a candidate cryptographic PRG) we show how to transform the randomized algorithm into an efficient deterministic one. This follows from new PRGs and targeted PRGs for space-bounded algorithms, which we combine with novel space-efficient evaluation methods. A central ingredient in all our constructions is hardness amplification reductions in logspace-uniform TC0, that were not known before.

Original languageEnglish
Title of host publication38th Computational Complexity Conference, CCC 2023
EditorsAmnon Ta-Shma
ISBN (Electronic)9783959772822
DOIs
StatePublished - 1 Jul 2023
Event38th Computational Complexity Conference, CCC 2023 - Warwick, United Kingdom
Duration: 17 Jul 202320 Jul 2023

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume264

Conference

Conference38th Computational Complexity Conference, CCC 2023
Country/TerritoryUnited Kingdom
CityWarwick
Period17/07/2320/07/23

Keywords

  • catalytic space
  • derandomization
  • space-bounded computation

All Science Journal Classification (ASJC) codes

  • Software

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