NP-Completeness and Disjoint NP-Pairs

نویسندگان

  • Christian Glaßer
  • Alan L. Selman
  • Samik Sengupta
  • Liyu Zhang
چکیده

We study the question of whether the class DisjNP of disjoint pairs (A,B) of NPsets contains a complete pair. The question relates to the question of whether optimal proof systems exist, and we relate it to the previously studied question of whether there exists a disjoint pair of NP-sets that is NP-hard. We show under reasonable hypotheses that nonsymmetric disjoint NP-pairs exist, which provides additional evidence for the existence of P-inseparable disjoint NP-pairs. We construct an oracle relative to which the class of disjoint NP-pairs does not have a complete pair, an oracle relative to which optimal proof systems exist, hence complete pairs exist, but no pair is NP-hard, and an oracle relative to which complete pairs exist, but optimal proof systems do not exist.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Disjoint NP - Pairs ( Extended

We study the question of whether the class D of disjoint pairs (A,B) of NP-sets contains a complete pair. The question relates to the question of whether optimal proof systems exist, and we relate it to the previously studied question of whether there exists a disjoint pair of NP-sets that is NP-hard. We show under reasonable hypotheses that nonsymmetric disjoint NP-pairs exist, which provides ...

متن کامل

On Reducibility and Symmetry of Disjoint NP-Pairs

We consider some problems about pairs of disjoint NP sets. The theory of these sets with a natural concept of reducibility is, on the one hand, closely related to the theory of proof systems for propositional calculus, and, on the other, it resembles the theory of NP completeness. Furthermore, such pairs are important in cryptography. Among others, we prove that the Broken Mosquito Screen pair ...

متن کامل

Disjoint NP-Pairs

We study the question of whether the class DisNP of disjoint pairs (A,B) of NP-sets contains a complete pair. The question relates to the question of whether optimal proof systems exist, and we relate it to the previously studied question of whether there exists a disjoint pair of NP-sets that is NP-hard. We show under reasonable hypotheses that nonsymmetric disjoint NP-pairs exist, which provi...

متن کامل

The Informational Content of Canonical Disjoint NP-Pairs

We investigate the connection between propositional proof systems and their canonical pairs. It is known that simulations between proof systems translate to reductions between their canonical pairs. We focus on the opposite direction and study the following questions. Q1: Where does the implication [can(f) ≤ m can(g) ⇒ f ≤s g] hold, and where does it fail? Q2: Where can we find proof systems of...

متن کامل

On the Deduction Theorem and Complete Disjoint NP-Pairs

In this paper we ask the question whether the extended Frege proof system EF satisfies a weak version of the deduction theorem. We prove that if this is the case, then complete disjoint NP-pairs exist. On the other hand, if EF is an optimal proof system, then the weak deduction theorem holds for EF . Hence the weak deduction property for EF is a natural intermediate condition between the optima...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2006