ECCC-Report TR24-023https://eccc.weizmann.ac.il/report/2024/023Comments and Revisions published for TR24-023en-usSun, 11 Feb 2024 07:50:41 +0200
Paper TR24-023
| Probabilistically Checkable Reconfiguration Proofs and Inapproximability of Reconfiguration Problems |
Shuichi Hirahara,
Naoto Ohsaka
https://eccc.weizmann.ac.il/report/2024/023Motivated 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 $\epsilon > 0$.Sun, 11 Feb 2024 07:50:41 +0200https://eccc.weizmann.ac.il/report/2024/023