# Questions tagged [query-complexity]

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### Complexity of approximating a real function using queries

Consider the following computational problem, where $I$ is the real interval $[-1,1]$: There is a monotonically-increasing function $f: I\to I$. You are allowed to access it only through queries of ...
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### Non-rigid isomorphic structures

In many of the problems trying to solve hidden shift over some objects like graphs mainly the rigid classes are considered. For eg. in this and this isomorphism problem restricted over rigid graphs is ...
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### Query complexity for functions $f\colon\left\{0,1\right\}^n\to\left\{0,1\right\}^m$

I'm studying query complexity and I'm trying to understand Bernstein-Vazirani's problem (https://en.wikipedia.org/wiki/Bernstein%E2%80%93Vazirani_algorithm) and Simon's problem (https://en.wikipedia....
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### Quantum evasiveness conjecture?

A property of simple $n$-vertex graphs is said to be evasive if its deterministic query complexity is exactly maximal, $\binom{n}{2}$ (that is, the best algorithm must query all $\binom{n}{2}$ ...
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### decision tree complexity and query complexity

I want good sources for starting with decision tree complexity and query complexity , what papers to start with ? what book chapters to read ? I already seen arora and barak book and I begin to read ...
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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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### Tolerance parameter of statistical query model and adaptivity

It seems that the reasonable assumption for the tolerance parameter of statistical query model is roughly $1/\sqrt{n}$, which is obtained from concentration inequalities (see, e.g., Definition 2.3 of ...
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### Does MCMC belong to the statistical query model?

It is known that a wide range of algorithms fall into the statistical query (SQ) learning model by Michael Kearns. Examples include k-means, logistic regression, naive Bayes (NB), SVM, ICA, PCA, ...
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### Las Vegas vs Monte Carlo randomized decision tree complexity

Background: Decision tree complexity or query complexity is a simple model of computation defined as follows. Let $f:\{0,1\}^n\to \{0,1\}$ be a Boolean function. The deterministic query complexity of ...
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### Information complexity of query algorithms?

Information complexity has been a very useful tool in communication complexity, mainly used to lower bound the communication complexity of distributed problems. Is there an analogue of information ...
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### What are the most fundamental metrics (criterions) of database performance?

I'm a student working on my thesis in database theory and looking for some research in the field of formal models of database performance and couldn't find any works in this area. I'm interested: what ...
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### How can one find the “hard” probability distribution on the input for recursive boolean functions?

Update: Since, it seems there is no progress regarding this question, any idea, conjecture, hunch, or advice is welcome. For example, are there any partial or incomplete results? What are the main ...
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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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### Delegating all of the work to the prover in $\mathcal{MA}$ protocols

An $\mathcal{MA}$ communication complexity protocol is communication complexity protocol that starts with an omniscient prover that sends a proof (that depends on the the specific input of the players,...
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### Are provable quantum speed-ups possible for classes larger than NP?

In the oracle query model quantum computers can provably achieve a quadratic speed-up over any classical randomized computer [Grover, BBBV]. Are similar speed-ups provably possible for higher levels ...
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### Natural, untestable graph properties

In graph property testing, an algorithm queries a target graph for the presence or absence of edges and needs to determine whether the target either has a certain property or is $\epsilon$-far from ...
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### Can quantum algorithms with exponential speed-up be rederived using span-programs?

The general adversary lower-bound is now known to characterize quantum query complexity due to breakthrough work by Reichardt et al. The same line of work also establishes connections to the span ...
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### Rigorous proof that a random function and a random permutation cannot be distinguished in polynomial time

I have a background in number theory and I'm trying to learn how to reason rigorously about algorithms. I'm reading chapter 2 of Katz and Lindell's Introduction to Modern Cryptography. Show that no ...
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### Is there a lower bound for the decisional Grover search problem?

What is known about the decisional version of the search problem? By decisional version of the search problem, I mean the problem in which you wish to determine whether there are $0$, or exactly $t$ ...
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### Models of computation strictly between classical and quantum in terms of query complexity

It is well known quantum computers are strictly more powerful than their classical counterparts in terms of query complexity. Are there other models (natural or artificial) that are strictly ...
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### Trade off between time and query complexity for total functions

This is a continuation of an earlier question on the trade off between time and query complexity. By a trade off we consider the following two types of algorithms: The best query algorithm: this ...
193 views