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
This research is published as the field of AI continues to explore fundamental algorithms and their limitations for practical applications.
It highlights a significant theoretical barrier for current AI systems, suggesting that converting decision-making algorithms into practical search solutions remains a hard problem in computational complexity.
The perceived effectiveness of certain foundational AI algorithmic approaches (BLP, AIP) for real-world search problems is diminished, indicating a need for new methods.
- · Researchers exploring alternative AI search algorithms
- · AI fields less reliant on specific integer programming relaxations for search
- · AI developers relying on BLP/AIP for complex search tasks
- · Projects expecting easy adaptation of decision-making algorithms to search
Further research funds may be directed towards developing novel search algorithms or techniques to bridge the gap between decision and search problems in AI.
The development trajectory of AI agents, which often require robust search capabilities, might face greater foundational challenges than previously understood.
This theoretical limitation could contribute to slower-than-expected progress in autonomous AI systems that need to perform complex real-world search and planning.
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Read at arXiv cs.CL