On provably disjoint NP-pairs

Alexander A. Razborov

November 1994


In this paper we study the pairs (U,V) of disjoint NP-sets representable in a theory T of Bounded Arithmetic in the sense that T proves tex2html_wrap_inline34. For a large variety of theories T we exhibit a natural disjoint NP-pair which is complete for the class of disjoint NP-pairs representable in T. This allows us to clarify the approach to showing independence of central open questions in Boolean complexity from theories of Bounded Arithmetic initiated in [1]. Namely, in order to prove the independence result from a theory T, it is sufficient to separate the corresponding complete NP-pair by a (quasi)poly-time computable set. We remark that such a separation is obvious for the theory tex2html_wrap_inline42 considered in [1], and this gives an alternative proof of the main result from that paper.

[1] A. Razborov. Unprovability of lower bounds on circuit size in certain fragments of Bounded Arithmetic. To appear in Izvestiya of the RAN, 1994.

Available as PostScript, PDF, DVI.


Last modified: 2003-06-08 by webmaster.