Related papers: Direct sum theorems beyond query complexity
To answer database queries over incomplete data the gold standard is finding certain answers: those that are true regardless of how incomplete data is interpreted. Such answers can be found efficiently for conjunctive queries and their…
We study the query complexity analogue of the class TFNP of total search problems. We give a way to convert partial functions to total search problems under certain settings; we also give a way to convert search problems back into partial…
Computational complexity is a core theory of computer science, which dictates the degree of difficulty of computation. There are many problems with high complexity that we have to deal, which is especially true for AI. This raises a big…
Given a conjunctive query $Q$ and a database $D$, a direct access to the answers of $Q$ over $D$ is the operation of returning, given an index $k$, the $k$-th answer for some order on its answers. While this problem is $\#\mathcal{P}$-hard…
Recurrence equations have played a central role in static cost analysis, where they can be viewed as abstractions of programs and used to infer resource usage information without actually running the programs with concrete data. Such…
Two-sample hypothesis testing for network comparison presents many significant challenges, including: leveraging repeated network observations and known node registration, but without requiring them to operate; relaxing strong structural…
For any function $f: X \times Y \to Z$, we prove that $Q^{*\text{cc}}(f) \cdot Q^{\text{OIP}}(f) \cdot (\log Q^{\text{OIP}}(f) + \log |Z|) \geq \Omega(\log |X|)$. Here, $Q^{*\text{cc}}(f)$ denotes the bounded-error communication complexity…
This is the full version of a paper submitted to the Computability in Europe (CiE 2023) conference, with all proofs omitted there. In 2012 P. D. Azar and S. Micali introduced a new model of interactive proofs, called "Rational Interactive…
Derived datasets can be defined implicitly or explicitly. An implicit definition (of dataset O in terms of datasets I) is a logical specification involving two distinguished sets of relational symbols. One set of relations is for the…
Neural networks and other machine learning models compute continuous representations, while humans communicate with discrete symbols. Reconciling these two forms of communication is desirable to generate human-readable interpretations or to…
We consider an instance of the following problem: Parties P_1,..., P_k each receive an input x_i, and a coordinator (distinct from each of these parties) wishes to compute f(x_1,..., x_k) for some predicate f. We are interested in one-round…
We consider several models of 1-round classical and quantum communication, some of these models have not been defined before. We "almost separate" the models of simultaneous quantum message passing with shared entanglement and the model of…
We study a new framework for property testing of probability distributions, by considering distribution testing algorithms that have access to a conditional sampling oracle.* This is an oracle that takes as input a subset $S \subseteq [N]$…
The Forrelation problem, introduced by Aaronson [A10] and Aaronson and Ambainis [AA15], is a well studied problem in the context of separating quantum and classical models. Variants of this problem were used to give exponential separations…
We study ranked enumeration of join-query results according to very general orders defined by selective dioids. Our main contribution is a framework for ranked enumeration over a class of dynamic programming problems that generalizes…
Abstraction is a well-known approach to simplify a complex problem by over-approximating it with a deliberate loss of information. It was not considered so far in Answer Set Programming (ASP), a convenient tool for problem solving. We…
Aaronson and Ambainis (SICOMP `18) showed that any partial function on $N$ bits that can be computed with an advantage $\delta$ over a random guess by making $q$ quantum queries, can also be computed classically with an advantage $\delta/2$…
We study the problem of robust forecast aggregation: combining expert forecasts with provable accuracy guarantees compared to the best possible aggregation of the underlying information. Prior work shows strong impossibility results, e.g.…
Scientists have demonstrated that quantum computing has presented novel approaches to address computational challenges, each varying in complexity. Adapting problem-solving strategies is crucial to harness the full potential of quantum…
The real numbers, it is taught at universities, correspond to our idea of a continuum, although the hyperreal numbers are located ``in between'' the real numbers. The number $x + dx$, where $dx$ should be an infinitesimal number and $x$…