Query complexity is a model of computation in which we have to compute a function f (x 1,…,
x N) of variables xi which can be accessed via queries. The complexity of an algorithm is …

In 1986, Saks and Wigderson conjectured that the largest separation between deterministic
and zero-error randomized query complexity for a total Boolean function is given by the …

We show that deterministic communication complexity can be superlogarithmic in the
partition number of the associated communication matrix. We also obtain near-optimal …

We show that randomized communication complexity can be superlogarithmic in the
partition number of the associated communication matrix, and we obtain near-optimal …

We establish two results regarding the query complexity of bounded-error randomized
algorithms.* Bounded-error separation theorem. There exists a total function $ f:\{0, 1\} …

A fundamental question in computer science is:\emph {Is it harder to solve $ n $ instances
independently than to solve them simultaneously?} This question, known as the direct sum …

The role of symmetry in Boolean functions $ f:\{0, 1\}^ n\to\{0, 1\} $ has been extensively
studied in complexity theory. For example, symmetric functions, that is, functions that are …

Saks and Wigderson in Proceedings of the 27 th FOCS, IEEE Computer Society, Los
Alamitos, CA, 1986, pp. 29--38 conjectured that R_0(f)=Ω(D(f)^0.753...) for all Boolean …

Herein, we investigate the zero-error randomized complexity, which is the least cost against
the worst input, of AND-OR tree computation by imposing various restrictions on the …

Boolean functions are one of the central objects in the study of Computer Science. Any
decision problem can be expressed as a Boolean function that takes an $ n $-bit string as …