Year: 2025
Type: article
Abstract: We obtain new catalytic algorithms for space-bounded derandomization. In the catalytic computation model introduced by (Buhrman, Cleve, Koucký, Loff, and Speelman STOC 2013), we are given a small worktape, and a larger catalytic tape that has an arbitrary initial configuration. We may edit this tape, but it must be exactly restored to its initial configuration at the completion of the computation. We prove that $$BPSPACE[S] \subseteq CSPACE[{S},{S^2}]$$ B P S P A C E [ S ] ⊆ C S P A C E [ S , S 2 ] where $$BPSPACE[S]$$ B P S P A C E [ S ] corresponds to randomized space S computation, and $$CSPACE[{S},{C}]$$ C S P A C E [ S , C ] corresponds to catalytic algorithms that use O(S) bits of workspace and O(C) bits of catalytic space. Previously, only $$BPSPACE[S]\subseteq CSPACE[{S},{2^{O(S)}}]$$ B P S P A C E [ S ] ⊆ C S P A C E [ S , 2 O ( S ) ] was known. In fact, we prove a general tradeoff, that for every $$\alpha \in [1,1.5]$$ α ∈ [ 1 , 1.5 ] , $$BPSPACE[S] \subseteq CSPACE[{S^{\alpha}},{S^{3-\alpha}}].$$ B P S P A C E [ S ] ⊆ C S P A C E [ S α , S 3 - α ] . We do not use the algebraic techniques of prior work on catalytic computation. Instead, we develop an algorithm that branches based on if the catalytic tape is conditionally random, and instantiate this primitive in a recursive framework. Our result gives
Source: Computational Complexity
Author: Edward Pyne
Institution: Massachusetts Institute of Technology
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
OpenAlex ID: W4414408661