Marek Karpinski, Rutger Verbeek

In contrast to deterministic or nondeterministic computation, it is

a fundamental open problem in randomized computation how to separate

different randomized time classes (at this point we do not even know

how to separate linear randomized time from ${\mathcal O}(n^{\log n})$

randomized time) or how to ...
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Shai Ben-David, Anna Gringauze.

We investigate sufficient conditions for the existence of

optimal propositional proof systems (PPS).

We concentrate on conditions of the form CoNF = NF.

We introduce a purely combinatorial property of complexity classes

- the notions of {\em slim} vs. {\em fat} classes.

These notions partition the ...
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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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Scott Aaronson, Avi Wigderson

Any proof of P!=NP will have to overcome two barriers: relativization

and natural proofs. Yet over the last decade, we have seen circuit

lower bounds (for example, that PP does not have linear-size circuits)

that overcome both barriers simultaneously. So the question arises of

whether there ...
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Scott Aaronson

Whether the class QMA (Quantum Merlin Arthur) is equal to QMA1, or QMA with one-sided error, has been an open problem for years. This note helps to explain why the problem is difficult, by using ideas from real analysis to give a "quantum oracle" relative to which QMA and QMA1 ... more >>>

Nikolay Vereshchagin

The Merlin-Arthur class of languages MA is included into Arthur-Merlin class AM, and into PP. For a standard transformation of a given MA protocol with Arthur's message (= random string) of length $a$ and Merlin's message of length $m$ to a PP machine, the latter needs $O(ma)$ random bits. The ... more >>>