Proves that NP_∞(R) for commutative semiring R equals weighted existential second-order logic with semiring-annotated relations, using an improved SRTM model that also reclaims prior results.
r (πn(π)−1) →c π n(π)it holds that JαKR(I)= ⊕ π′,s.t.cπ i =cπ′ i r(π′ 1)⊗...⊗r(π′ n(π′)−1)
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Fagin's Theorem for Semiring Turing Machines
Proves that NP_∞(R) for commutative semiring R equals weighted existential second-order logic with semiring-annotated relations, using an improved SRTM model that also reclaims prior results.