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### Randomized and deterministic query complexity of symmetric functions

The deterministic query complexity $D(f)$ of a symmetric function $f$ is $\Omega(n)$ (except for f = 0 or f = 1). I am wondering if the same result holds for the (bounded-error) randomized query ...
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### Discovering a graph with minimal oracle queries

I have a transitive DAG G which is a subgraph of an unknown DAG R. (The nodes are the same in G and R, but R may have edges not in G.) I can determine the presence of a given edge in R by an oracle ...
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### Trade off between width and depth of free BDDs for total functions

Terminology A binary decision diagram is a directed acyclic graph with one source (root), and two sinks ($A$ and $B$). Each non-sink nodes is labeled by an integer $i \in \{1,...,n\}$ and has out-...
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### Algorithm for optimizing decision trees

Background A binary decision tree $T$ is a rooted tree where each internal node (and root) is labeled by an index $j \in \{1,..., n\}$ such that no path from root to leaf repeats an index, the leafs ...
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### Trade off between time and query complexity

Working directly with time complexity or circuit lower bounds is scary. Hence, we develop tools like query complexity (or decision-tree complexity) to get a handle on lower bounds. Since each query ...
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### Using the extra power of the negative adversary method

The negative adversary method ($ADV^\pm$) is an SDP that characterizes quantum query complexity. It is a generalization of the widely used adversary method ($ADV$), and overcomes the two barriers that ...
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### Bounding the gap between quantum and deterministic query complexity

Although exponential separations between bounded-error quantum query complexity ($Q(f)$) and deterministic query complexity ($D(f)$) or bounded-error randomized query complexity ($R(f)$) are known, ...
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### Span programs, witness size, and certificate complexity

A span program is a linear-algebraic way of specifying a boolean function introduced here. Recently, this model was used to show that the negative adversary method provides a tight characterization (...
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### Quantum query complexity and certificate complexity

A certificate for an input $x$ is a subset of bits $S \subseteq \{1,...,n\}$ such that for all inputs $y$, $(\forall i \in S \quad y_i = x_i) \rightarrow f(y) = f(x)$. Then $C_x(f)$ is the minimum ...