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In this paper we present a Hashed-Path Traveling Salesperson Problem (HPTSP),a new type of problem which has the interesting property of having nopolynomial time solutions. Next we show that HPTSP is in the class NP bydemonstrating that local information about sub-routes is insufficient tocompute the complete value of each route. As a consequence, via Ladner'stheorem, we show that the class NPI is non-empty.

Construction of an NP Problem with an Exponential Lower Bound