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Data exchange heavily relies on the notion of incomplete database instances. Several semantics for such instances have been proposed and include open (OWA), closed (CWA), and open-closed (OCWA) world. For all these semantics important…
In one of our earlier works, we proposed to approximate Pareto fronts to multiobjective optimization problems by two-sided approximations, one from inside and another from outside of the feasible objective set, called, respectively, lower…
We consider partially ordered sets of combinatorial structures under consecutive orders, meaning that two structures are related when one embeds in the other such that `consecutive' elements remain consecutive in the image. Given such a…
A perfect number is a positive integer $N$ such that the sum of all the positive divisors of $N$ equals $2N$, denoted by $\sigma(N) = 2N$. The question of the existence of odd perfect numbers (OPNs) is one of the longest unsolved problems…
In the nineties Immerman and Medina initiated the search for syn- tactic tools to prove NP-completeness. In their work, amongst several results, they conjecture that the NP-completeness of a problem defined by the conjunction of a sentence…
Shellings of simplicial complexes have long been a useful tool in topological and algebraic combinatorics. Shellings of a complex expose a large amount of information in a helpful way, but are not easy to construct, often requiring deep…
To combine and query ordered data from multiple sources, one needs to handle uncertainty about the possible orderings. Examples of such "order-incomplete" data include integrated event sequences such as log entries, lists of properties…
Queries with aggregation and arithmetic operations, as well as incomplete data, are common in real-world database, but we lack a good understanding of how they should interact. On the one hand, systems based on SQL provide ad-hoc rules for…
Bennett's notion of depth is usually considered to describe the usefulness and internal organization of the information encoded into an object such as an infinite binary sequence. We consider a natural way to relativize the notion of depth…
The arithmetical hierarchy (AH) is similar to the polynomial hierarchy (PH). Unlike the PH, the AH does not collapse relative to any oracle. A language in the (k + 1)-st level of the AH is computable enumerable (c.e.) relative to the kth…
Whilst Power Kripke-Platek set theory, KPP, shares many properties with ordinary Kripke-Platek set theory, KP, in several ways it behaves quite differently from KP. This is perhaps most strikingly demonstrated by a result, due to Mathias,…
The oracle c.c.c. is closely related to Cohen forcing. During an iteration we can ``omit a type''; i.e. preserve ``the intersection of a given family of Borel sets of reals is empty'' provided that Cohen forcing satisfies it. We generalize…
We consider the problem of minimizing a smooth, Lipschitz, convex function over a compact, convex set using sub-zeroth-order oracles: an oracle that outputs the sign of the directional derivative for a given point and a given direction, an…
The issue of honesty in constructing confidence sets arises in nonparametric regression. While optimal rate in nonparametric estimation can be achieved and utilized to construct sharp confidence sets, severe degradation of confidence level…
Classical approaches for OLAP assume that the data of all tables is complete. However, in case of incomplete tables with missing tuples, classical approaches fail since the result of a SQL aggregate query might significantly differ from the…
We observe $(X_i,Y_i)_{i=1}^n$ where the $Y_i$'s are real valued outputs and the $X_i$'s are $m\times T$ matrices. We observe a new entry $X$ and we want to predict the output $Y$ associated with it. We focus on the high-dimensional…
We construct orthogonal arrays OA$_{\lambda} (k,n)$ (of strength two) having a row that is repeated $m$ times, where $m$ is as large as possible. In particular, we consider OAs where the ratio $m / \lambda$ is as large as possible; these…
Many classical theorems in combinatorics establish the emergence of substructures within sufficiently large collections of objects. Well-known examples are Ramsey's theorem on monochromatic subgraphs and the Erd\H{o}s-Rado sunflower lemma.…
What is the minimum amount of information and time needed to solve 2SAT? When the instance is known, it can be solved in polynomial time, but is this also possible without knowing the instance? Bei, Chen and Zhang (STOC '13) considered a…
We show that quantum oracles provide an advantage over classical oracles for answering classical counterfactual questions in causal models, or equivalently, for identifying unknown causal parameters such as distributions over functional…