All reports by Author Alan L. Selman:

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TR07-018
| 1st March 2007
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Christian Glaßer, Alan L. Selman, Liyu Zhang#### The Informational Content of Canonical Disjoint NP-Pairs

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TR06-090
| 22nd June 2006
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Christian Glaßer, Alan L. Selman, Stephen Travers, Liyu Zhang#### Non-Mitotic Sets

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TR06-069
| 11th May 2006
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Christian Glaßer, Alan L. Selman, Stephen Travers, Klaus W. Wagner#### The Complexity of Unions of Disjoint Sets

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TR05-072
| 11th July 2005
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Christian Glaßer, Alan L. Selman, Liyu Zhang#### Survey of Disjoint NP-Pairs and Relations to Propositional Proof Systems

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TR05-068
| 7th July 2005
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Christian Glaßer, A. Pavan, Alan L. Selman, Liyu Zhang#### Redundancy in Complete Sets

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TR05-011
| 21st December 2004
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Christian Glaßer, Mitsunori Ogihara, A. Pavan, Alan L. Selman, Liyu Zhang#### Autoreducibility, Mitoticity, and Immunity

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TR04-106
| 19th November 2004
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Christian Glaßer, Alan L. Selman, Liyu Zhang#### Canonical Disjoint NP-Pairs of Propositional Proof Systems

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TR04-019
| 15th January 2004
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Christian Glaßer, A. Pavan, Alan L. Selman, Samik Sengupta#### Properties of NP-Complete Sets

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TR04-007
| 13th January 2004
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Alan L. Selman, Samik Sengupta#### Polylogarithmic-round Interactive Proofs for coNP Collapses the Exponential Hierarchy

Revisions: 1
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Comments: 1

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TR03-027
| 21st April 2003
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Christian Glaßer, Alan L. Selman, Samik Sengupta#### Reductions between Disjoint NP-Pairs

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TR03-011
| 17th February 2003
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Christian Glaßer, Alan L. Selman, Samik Sengupta, Liyu Zhang#### Disjoint NP-Pairs

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TR02-005
| 3rd January 2002
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A. Pavan, Alan L. Selman#### Bi-Immunity Separates Strong NP-Completeness Notions

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TR01-032
| 3rd April 2001
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A. Pavan, Alan L. Selman#### Separation of NP-completeness Notions

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TR96-027
| 20th February 1996
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Lane A. Hemaspaandra, Ashish Naik, Mitsunori Ogihara, Alan L. Selman#### Computing Solutions Uniquely Collapses the Polynomial Hierarchy

Christian Glaßer, Alan L. Selman, Liyu Zhang

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 >>>

Christian Glaßer, Alan L. Selman, Stephen Travers, Liyu Zhang

<p> We study the question of the existence of non-mitotic sets in NP. We show under various hypotheses that:</p>

<ul>

<li>1-tt-mitoticity and m-mitoticity differ on NP.</li>

<li>1-tt-reducibility and m-reducibility differ on NP.</li>

<li>There exist non-T-autoreducible sets in NP (by a result from Ambos-Spies, these sets are neither ...
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Christian Glaßer, Alan L. Selman, Stephen Travers, Klaus W. Wagner

This paper is motivated by the open question

whether the union of two disjoint NP-complete sets always is

NP-complete. We discover that such unions retain

much of the complexity of their single components. More precisely,

they are complete with respect to more general reducibilities.

Christian Glaßer, Alan L. Selman, Liyu Zhang

We survey recent results on disjoint NP-pairs. In particular, we survey the relationship of disjoint NP-pairs to the theory of proof systems for propositional calculus.

more >>>Christian Glaßer, A. Pavan, Alan L. Selman, Liyu Zhang

We show that a set is m-autoreducible if and only if it is m-mitotic. This solves a long standing open question in a surprising way. As a consequence of this unconditional result and recent work by Glasser et al., complete sets for all of the following complexity classes are m-mitotic: ... more >>>

Christian Glaßer, Mitsunori Ogihara, A. Pavan, Alan L. Selman, Liyu Zhang

We show the following results regarding complete sets:

NP-complete sets and PSPACE-complete sets are many-one

autoreducible.

Complete sets of any level of PH, MODPH, or

the Boolean hierarchy over NP are many-one autoreducible.

EXP-complete sets are many-one mitotic.

NEXP-complete sets are weakly many-one mitotic.

PSPACE-complete sets are weakly Turing-mitotic.

... more >>>Christian Glaßer, Alan L. Selman, Liyu Zhang

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 ...
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Christian Glaßer, A. Pavan, Alan L. Selman, Samik Sengupta

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 ...
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Alan L. Selman, Samik Sengupta

It is known \cite{BHZ87} that if every language in coNP has a

constant-round interactive proof system, then the polynomial hierarchy

collapses. On the other hand, Lund {\em et al}.\ \cite{LFKN92} have shown that

#SAT, the #P-complete function that outputs the number of satisfying

assignments of a Boolean ...
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Christian Glaßer, Alan L. Selman, Samik Sengupta

We prove that all of the following assertions are equivalent:

There is a many-one complete disjoint NP-pair;

there is a strongly many-one complete disjoint NP-pair;

there is a Turing complete disjoint NP-pair such that all reductions

are smart reductions;

there is a complete disjoint NP-pair for one-to-one, invertible ...
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Christian Glaßer, Alan L. Selman, Samik Sengupta, Liyu Zhang

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 ...
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A. Pavan, Alan L. Selman

We prove that if for some epsilon > 0 NP contains a set that is

DTIME(2^{n^{epsilon}})-bi-immune, then NP contains a set that 2-Turing

complete for NP but not 1-truth-table complete for NP. Lutz and Mayordomo

(LM96) and Ambos-Spies and Bentzien (AB00) previously obtained the

same consequence using strong ...
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A. Pavan, Alan L. Selman

We use hypotheses of structural complexity theory to separate various

NP-completeness notions. In particular, we introduce an hypothesis from which we describe a set in NP that is Turing complete but not truth-table complete. We provide fairly thorough analyses of the hypotheses that we introduce. Unlike previous approaches, we ...
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Lane A. Hemaspaandra, Ashish Naik, Mitsunori Ogihara, Alan L. Selman

Is there an NP function that, when given a satisfiable formula

as input, outputs one satisfying assignment uniquely? That is, can a

nondeterministic function cull just one satisfying assignment from a

possibly exponentially large collection of assignments? We show that if

there is such a nondeterministic function, then the polynomial ...
more >>>