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 $k\geq3$.

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Parameterized Resolution and, moreover, a general framework for parameterized proof complexity was introduced by Dantchev, Martin, and Szeider (FOCS'07). In that paper, Dantchev et al. show a complexity gap in tree-like Parameterized Resolution for propositional formulas arising from translations of first-order principles.
We broadly investigate Parameterized Resolution obtaining the following ... more >>>

We present a general notion of properties that
are characterized by local conditions that are invariant
under a sufficiently rich class of symmetries.
Our framework generalizes two popular models of
testing graph properties as well as the algebraic
invariances studied by Kaufman and Sudan (STOC'08).

We show that, in the ... more >>>