Ineffectiveness for Search and Undecidability of PCSP Meta-Problems

arXiv:2504.04639v4 Announce Type: replace-cross Abstract: It is an open question whether the search and decision versions of promise CSPs are equivalent. Most known algorithms for PCSPs solve only their \emph{decision} variant, and it is unknown whether they can be adapted to solve \emph{search} as well. The main approaches, called BLP, AIP and BLP+AIP, handle a PCSP by finding a solution to a relaxation of some integer program. We prove that rounding those solutions to a proper search certificate can be as hard as any problem in the class TFNP. In other words, these algorithms are ineffective

Source: arXiv cs.CL — read the full report at the original publisher.

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