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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Anna Gal, Avi Wigderson

This paper provides logspace and small circuit depth analogs

of the result of Valiant-Vazirani, which is a randomized (or

nonuniform) reduction from NP to its arithmetic analog ParityP.

We show a similar randomized reduction between the

Boolean classes NL and semi-unbounded fan-in Boolean circuits and

their arithmetic counterparts. These ...
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Oded Goldreich, Madhu Sudan

Locally testable codes are error-correcting codes that admit

very efficient codeword tests. Specifically, using a constant

number of (random) queries, non-codewords are rejected with

probability proportional to their distance from the code.

Locally testable codes are believed to be the combinatorial

core of PCPs. However, the relation is ...
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Mohammad Mahmoody, David Xiao

The closure of complexity classes is a elicate question and the answer varies depending on the type of reduction considered. The closure of most classes under many-to-one (Karp) reductions is clear, but the question becomes complicated when oracle (Cook) reductions are allowed, and even more so when the oracle reductions ... more >>>

Daniele Micciancio

We prove that the Shortest Vector Problem (SVP) on point lattices is NP-hard to approximate for any constant factor under polynomial time reverse unfaithful random reductions. These are probabilistic reductions with one-sided error that produce false negatives with small probability, but are guaranteed not to produce false positives regardless of ... more >>>

Shuichi Hirahara, Osamu Watanabe

The Minimum Circuit Size Problem (MCSP) is known to be hard for statistical zero knowledge via a BPP-reduction (Allender and Das, 2014), whereas establishing NP-hardness of MCSP via a polynomial-time many-one reduction is difficult (Murray and Williams, 2015) in the sense that it implies ZPP $\neq$ EXP, which is a ... more >>>

Michael Saks, Rahul Santhanam

We study the power of randomized polynomial-time non-adaptive reductions to the problem of approximating Kolmogorov complexity and its polynomial-time bounded variants.

As our first main result, we give a sharp dichotomy for randomized non-adaptive reducibility to approximating Kolmogorov complexity. We show that any computable language $L$ that has a randomized ... more >>>