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Electronic Colloquium on Computational Complexity

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Reports tagged with MA:
TR10-060 | 5th April 2010
Dmitry Gavinsky, Alexander A. Sherstov

A Separation of NP and coNP in Multiparty Communication Complexity

We prove that NP$\ne$coNP and coNP$\nsubseteq$MA in the number-on-forehead model of multiparty communication complexity for up to $k=(1-\epsilon)\log n$ players, where $\epsilon>0$ is any constant. Specifically, we construct a function $F:(\zoon)^k\to\zoo$ with co-nondeterministic
complexity $O(\log n)$ and Merlin-Arthur
complexity $n^{\Omega(1)}$.
The problem was open for $k\geq3$.

more >>>

TR13-144 | 8th October 2013
VyasRam Selvam

The two queries assumption and Arthur-Merlin classes

We explore the implications of the two queries assumption, $P^{NP[1]}=P_{||}^{NP[2]}$, with respect to the polynomial hierarchy and the classes $AM$ and $MA$.
We prove the following results:

1. $P^{NP[1]}=P_{||}^{NP[2]}$ $\implies$ $AM = MA$
2. $P^{NP[1]}=P_{||}^{NP[2]}$ $\implies$ $PH \subset MA_{/1}$
3. $\exists\;B\;P^{NP[1]^B}=P^{NP[2]^B}$ and $NP^B \not\subseteq coMA^B$.
4. $P^{NP[1]}=P_{||}^{NP[2]}$ $\implies$ $PH ... more >>>

TR13-152 | 7th November 2013
Oded Goldreich, Avi Wigderson

On Derandomizing Algorithms that Err Extremely Rarely

Revisions: 2

{\em Does derandomization of probabilistic algorithms become easier when the number of ``bad'' random inputs is extremely small?}

In relation to the above question, we put forward the following {\em quantified derandomization challenge}:
For a class of circuits $\cal C$ (e.g., P/poly or $AC^0,AC^0[2]$) and a bounding function $B:\N\to\N$ (e.g., ... more >>>

TR20-043 | 29th March 2020
Dorit Aharonov, Alex Bredariol Grilo

A combinatorial MA-complete problem

Revisions: 2

Despite the interest in the complexity class MA, the randomized analog of NP, there is just a couple of known natural (promise-)MA-complete problems, the first due to Bravyi and Terhal (SIAM Journal of Computing 2009) and the second due to Bravyi (Quantum Information and Computation 2015). Surprisingly, both problems are ... more >>>

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