In this paper we study the pairs (UV) of disjoint NP-setsrepresentable in a theory T of Bounded Arithmetic in the sense thatT proves UV=. For a large variety of theories Twe exhibit a natural disjoint NP-pair which is complete for theclass of disjoint NP-pairs representable in T. This allows us toclarify the approach to showing independence of central open questions inBoolean complexity from theories of Bounded Arithmetic initiatedin cite{ind}. Namely, in order to prove the independence resultfrom a theory T, it is sufficient to separate the correspondingcomplete NP-pair by a (quasi)poly-time computable set. We remarkthat such a separation is obvious for the theory scrS(S2)+scrSb2?PIND considered in cite{ind}, and this gives analternative proof of the main result from that paper.
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