Over min-plus semirings, VNP equals VP with logarithmic complementations in certificates but not with superlogarithmic ones; width-3 ABPs compute all such problems while width-2 cannot, and hypercube sums over weak models reach VNP power.
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VP, VNP and Algebraic Branching Programs over Min-Plus Semirings
Over min-plus semirings, VNP equals VP with logarithmic complementations in certificates but not with superlogarithmic ones; width-3 ABPs compute all such problems while width-2 cannot, and hypercube sums over weak models reach VNP power.