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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Leonid Gurvits

Let $p(x_1,...,x_n) =\sum_{ (r_1,...,r_n) \in I_{n,n} } a_{(r_1,...,r_n) } \prod_{1 \leq i \leq n} x_{i}^{r_{i}}$

be homogeneous polynomial of degree $n$ in $n$ real variables with integer nonnegative coefficients.

The support of such polynomial $p(x_1,...,x_n)$

is defined as $supp(p) = \{(r_1,...,r_n) \in I_{n,n} : a_{(r_1,...,r_n)} \neq 0 ...
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Emanuele Viola

We prove several new results regarding the relationship between probabilistic time, BPTime(t), and alternating time, \Sigma_{O(1)} Time(t). Our main results are the following:

1) We prove that BPTime(t) \subseteq \Sigma_3 Time(t polylog(t)). Previous results show that BPTime(t) \subseteq \Sigma_2 Time(t^2 log t) (Sipser and Gacs, STOC '83; Lautemann, IPL '83) ... more >>>

Joao Marques-Silva, Mikolas Janota

Propositional Satisfiability (SAT) solvers are routinely used for

solving many function problems.

A natural question that has seldom been addressed is: what is the

best worst-case number of calls to a SAT solver for solving some

target function problem?

This paper develops tighter upper bounds on the query complexity of

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Titus Dose, Christian Glaßer

The article investigates the relation between three well-known hypotheses.

1) Hunion: the union of disjoint complete sets for NP is complete for NP

2) Hopps: there exist optimal propositional proof systems

3) Hcpair: there exist complete disjoint NP-pairs

The following results are obtained:

a) The hypotheses are pairwise independent ...
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