A Parsimonious Reduction from #SAT to Motif-Avoidant Attractors in Bounded-Fan-In AND-NOT Boolean Networks
Year: 2026
Type: preprint
Abstract: We construct an explicit polynomial-time parsimonious reduction from #SAT to counting motif-avoidant attractors of asynchronous Boolean networks. Each update is a conjunction of at most two signed literals or a constant, and the interaction graph has exactly one strongly connected component of size greater than one, comprising two nodes. We prove #MAA(N_phi) = #SAT(phi) by classifying terminal strongly connected components and minimal trap subcubes. Thus restricted MAA counting is #P-hard and restricted MAA existence is NP-hard. Two independent exhaustive finite verifiers corroborate the construction on small instances. Historical first-in-literature novelty has not been established; this is not a proof of P != NP, and full-class #P-completeness is not claimed. The accompanying source ZIP contains the full derivation, exact verification scripts and logs.
Author: Henry, Kias
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225320067