A Fine-Grained Complexity View on Propositional Abduction -- Algorithms and Lower Bounds

• URL: http://arxiv.org/abs/2505.10201v1
• Date: Thu, 15 May 2025 11:56:19 GMT
• Title: A Fine-Grained Complexity View on Propositional Abduction -- Algorithms and Lower Bounds
• Authors: Victor Lagerkvist, Mohamed Maizia, Johannes Schmidt,
• Abstract summary: We analyze the complexity of intractable abduction problems under the seemingly overlooked but natural parameter n.<n>We obtain several positive results for $SigmaP$ as well as NP- and coNP-complete fragments.<n>We complement this with lower bounds and for many fragments rule out improvements under the (strong) exponential-time hypothesis.
• Score: 6.6362553223890535
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The Boolean satisfiability problem (SAT) is a well-known example of monotonic reasoning, of intense practical interest due to fast solvers, complemented by rigorous fine-grained complexity results. However, for non-monotonic reasoning, e.g., abductive reasoning, comparably little is known outside classic complexity theory. In this paper we take a first step of bridging the gap between monotonic and non-monotonic reasoning by analyzing the complexity of intractable abduction problems under the seemingly overlooked but natural parameter n: the number of variables in the knowledge base. We obtain several positive results for $\Sigma^P_2$- as well as NP- and coNP-complete fragments, which implies the first example of beating exhaustive search for a $\Sigma^P_2$-complete problem (to the best of our knowledge). We complement this with lower bounds and for many fragments rule out improvements under the (strong) exponential-time hypothesis.

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