Motivated by the inapproximability of reconfiguration problems, we present a new PCP-type characterization of PSPACE, which we call a probabilistically checkable reconfiguration proof (PCRP): Any PSPACE computation can be encoded into an exponentially long sequence of polynomially long proofs such that every adjacent pair of the proofs differs in at most one bit, and every proof can be probabilistically checked by reading a constant number of bits. Using the new characterization, we prove PSPACE-completeness of approximate versions of many reconfiguration problems, such as the Maxmin $3$-SAT Reconfiguration problem. This resolves the open problem posed by Ito, Demaine, Harvey, Papadimitriou, Sideri, Uehara, and Uno (ISAAC 2008; Theor. Comput. Sci. 2011) as well as the Reconfiguration Inapproximability Hypothesis by Ohsaka (STACS 2023) affirmatively. We also present PSPACE-completeness of approximating the Maxmin Clique Reconfiguration problem to within a factor of $n^\epsilon$ for some constant $\epsilon > 0$.

翻译：受重配置问题不可近似性的启发，我们提出了一种新的PSPACE的PCP型刻画，称为概率可检验重配置证明（PCRP）：任意PSPACE计算均可编码为一个指数长的多项式长证明序列，使得相邻证明对最多仅有一位差异，且每个证明可通过读取常数个比特进行概率检验。利用这一新刻画，我们证明了许多重配置问题（如Maxmin $3$-SAT重配置问题）的近似版本的PSPACE完备性。这肯定性地解决了Ito、Demaine、Harvey、Papadimitriou、Sideri、Uehara和Uno（ISAAC 2008；Theor. Comput. Sci. 2011）提出的公开问题，以及Ohsaka（STACS 2023）的重配置不可近似性假设。我们还证明了在某个常数$\epsilon > 0$的因子$n^\epsilon$内近似Maxmin团重配置问题的PSPACE完备性。