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REPORTS > KEYWORD > DISJOINT NP-PAIRS:
Reports tagged with disjoint NP-pairs:
TR03-011 | 17th February 2003
Christian Glaßer, Alan L. Selman, Samik Sengupta, Liyu Zhang

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 ... more >>>

TR04-019 | 15th January 2004
Christian Glaßer, A. Pavan, Alan L. Selman, Samik Sengupta

Properties of NP-Complete Sets

We study several properties of sets that are complete for NP.
We prove that if $L$ is an NP-complete set and $S \not\supseteq L$ is a p-selective sparse set, then $L - S$ is many-one-hard for NP. We demonstrate existence of a sparse set $S \in \mathrm{DTIME}(2^{2^{n}})$
such ... more >>>

TR04-082 | 9th September 2004
Olaf Beyersdorff

Representable Disjoint NP-Pairs

Revisions: 1

We investigate the class of disjoint NP-pairs under different reductions.
The structure of this class is intimately linked to the simulation order
of propositional proof systems, and we make use of the relationship between
propositional proof systems and theories of bounded arithmetic as the main
tool of our analysis.
more >>>

TR04-106 | 19th November 2004
Christian Glaßer, Alan L. Selman, Liyu Zhang

Canonical Disjoint NP-Pairs of Propositional Proof Systems

We prove that every disjoint NP-pair is polynomial-time, many-one equivalent to
the canonical disjoint NP-pair of some propositional proof system. Therefore, the degree structure of the class of disjoint NP-pairs and of all canonical pairs is
identical. Secondly, we show that this degree structure is not superficial: Assuming there exist ... more >>>

TR05-077 | 15th July 2005

On a D-N-optimal acceptor for TAUT

The notion of an optimal acceptor for TAUT (the optimality
property is stated only for input strings from TAUT) comes from the line
of research aimed at resolving the question of whether optimal
propositional proof systems exist. In this paper we introduce two new
types of optimal acceptors, a D-N-optimal ... more >>>

TR05-083 | 24th July 2005
Olaf Beyersdorff

Disjoint NP-Pairs from Propositional Proof Systems

For a proof system P we introduce the complexity class DNPP(P)
of all disjoint NP-pairs for which the disjointness of the pair is
efficiently provable in the proof system P.
We exhibit structural properties of proof systems which make the
previously defined canonical NP-pairs of these proof systems hard ... more >>>

TR05-123 | 25th October 2005
Olaf Beyersdorff

Tuples of Disjoint NP-Sets

Disjoint NP-pairs are a well studied complexity theoretic concept with
important applications in cryptography and propositional proof
complexity.

In this paper we introduce a natural generalization of the notion of
disjoint NP-pairs to disjoint k-tuples of NP-sets for k>1.
We define subclasses of ... more >>>

TR06-142 | 26th October 2006
Olaf Beyersdorff

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, ... more >>>

TR07-018 | 1st March 2007
Christian Glaßer, Alan L. Selman, Liyu Zhang

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) \le_m can(g) => f \le_s ... more >>>

TR13-070 | 4th May 2013
Iddo Tzameret

On Sparser Random 3SAT Refutation Algorithms and Feasible Interpolation

Revisions: 1

We formalize a combinatorial principle, called the 3XOR principle, due to Feige, Kim and Ofek (2006), as a family of unsatisfiable propositional formulas for which refutations of small size in any propositional proof system that possesses the feasible interpolation property imply an efficient *deterministic* refutation algorithm for random 3SAT with ... more >>>

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