2026-08-18T16:45:06Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:23499 2025-10-02T12:56:56Z ddc:004 open_access

Yet Another Simple Proof of the PCRP Theorem Ohsaka, Naoto reconfiguration problems hardness of approximation probabilistic proof systems The Probabilistically Checkable Reconfiguration Proof (PCRP) theorem, proven by Hirahara and Ohsaka (STOC 2024) [Hirahara and Ohsaka, 2024] and Karthik C. S. and Manurangsi [{Karthik {C. S.}} and Manurangsi, 2023], provides a new PCP-type characterization of PSPACE: A language L is in PSPACE if and only if there exists a probabilistic verifier 𝒱 and a pair of polynomial-time computable proofs π^ini, π^end such that the following hold for every input x: - If x ∈ L, then π^ini(x) can be transformed into π^end(x) by repeatedly flipping a single bit of the proof at a time, while making 𝒱(x) to accept every intermediate proof with probability 1. - If x ∉ L, then any such transformation induces a proof that is rejected by 𝒱(x) with probability more than 1/2. The PCRP theorem finds many applications in PSPACE-hardness of approximation for reconfiguration problems. In this paper, we present an alternative proof of the PCRP theorem that is "simpler" than those of Hirahara and Ohsaka [Hirahara and Ohsaka, 2024] and Karthik C. S. and Manurangsi [Karthik C. S. and Manurangsi, 2023]. Our PCRP system is obtained by combining simple robustization and composition steps in a modular fashion, which renders its analysis more intuitive. The crux of implementing the robustization step is an error-correcting code that enjoys both list decodability and reconfigurability, the latter of which enables to reconfigure between a pair of codewords, while avoiding getting too close to any other codewords. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Naoto Ohsaka 2025 Is Part Of LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ICALP.2025.122 urn:nbn:de:0030-drops-234995 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.122 eng https://creativecommons.org/licenses/by/4.0/legalcode