Swagato Sanyal

The Zero-Error Randomized Query Complexity of the Pointer Function.

The pointer function of G{o}{o}s, Pitassi and Watson \cite{DBLP:journals/eccc/GoosP015a} and its variants have recently been used to prove separation results among various measures of complexity such as deterministic, randomized and quantum query complexities, exact and approximate polynomial degrees, etc. In particular, the widest possible (quadratic) separations between deterministic and zero-error randomized query complexity, as well as between bounded-error and zero-error randomized query complexity, have been obtained by considering {\em variants}~\cite{DBLP:journals/corr/AmbainisBBL15} of this pointer function. However, as was pointed out in \cite{DBLP:journals/corr/AmbainisBBL15}, the precise zero-error complexity of the original pointer function was not known. We show a lower bound of

A composition theorem for randomized query complexity

\widetilde{\Omega}(n^{3/4})

Quadratically Tight Relations for Randomized Query Complexity

on the zero-error randomized query complexity of the pointer function on

Separation Between Deterministic and Randomized Query Complexity

\Theta(n \log n)

Towards Better Separation between Deterministic and Randomized Query Complexity

bits; since an

A Composition Theorem via Conflict Complexity.

\widetilde{O}(n^{3/4})

Towards Better Separation between Deterministic and Randomized Query Complexity.

upper bound is already known \cite{DBLP:conf/fsttcs/MukhopadhyayS15}, our lower bound is optimal up to a factor of

Linear sketching over F 2

\polylog\, n

One-way Communication and Non-adaptive Decision Tree.

.

A Composition Theorem for Randomized Query complexity.

Let the randomized query complexity of a relation for error probability