Related papers: The Small-Is-Very-Small Principle
A {\it superpattern} is a string of characters of length $n$ that contains as a subsequence, and in a sense that depends on the context, all the smaller strings of length $k$ in a certain class. We prove structural and probabilistic results…
Existential rules are a positive fragment of first-order logic that generalizes function-free Horn rules by allowing existentially quantified variables in rule heads. This family of languages has recently attracted significant interest in…
The problem of reconstructing a sequence of independent and identically distributed symbols from a set of equal size, consecutive, fragments, as well as a dependent reference sequence, is considered. First, in the regime in which the…
This article precisely defines huge proofs within the system of Natural Deduction for the Minimal implicational propositional logic \mil. This is what we call an unlimited family of super-polynomial proofs. We consider huge families of…
A suffixient set is a novel combinatorial object that captures the essential information of repetitive strings in a way that, provided with a random access mechanism, supports various forms of pattern matching. In this paper, we study the…
Limited overlap between treated and control groups is a key challenge in observational analysis. Standard approaches like trimming importance weights can reduce variance but introduce a fundamental bias. We propose a sensitivity framework…
This paper proves the minimum size of a supersequence over a set of eight elements is 52. This disproves a conjecture that the lower bound of the supersequence is the partial sum of the geometric Connell sequence. By studying the internal…
The support of minimizing measures of the causal variational principle on the sphere is analyzed. It is proven that in the case $\tau>\sqrt{3}$, the support of every minimizing measure is contained in a finite number of real analytic curves…
The notion of weak truth-table reducibility plays an important role in recursion theory. In this paper, we introduce an elaboration of this notion, where a computable bound on the use function is explicitly specified. This elaboration…
We present a new fragment of axiomatic set theory for pure sets and for the iteration of power sets within given transitive sets. It turns out that this formal system admits an interesting hierarchy of models with true membership relation…
Over the past two decades, several consistent procedures have been designed to infer causal conclusions from observational data. We prove that if the true causal network might be an arbitrary, linear Gaussian network or a discrete Bayes…
Two results are presented concerning the entailment problem in Separation Logic with inductively defined predicate symbols and theory reasoning. First, we show that the entailment problem is undecidable for rules with bounded tree-width, if…
One of the consequences of the Compactness Principle in structural Ramsey theory is that the small Ramsey degrees cannot exceed the corresponding big Ramsey degrees, thereby justifying the choice of adjectives. However, it is unclear what…
This paper develops new limit theory for data that are generated by networks or more generally display cross-sectional dependence structures that are governed by observable and unobservable characteristics. Strategic network formation…
In this paper, we consider existential rules, an expressive formalism well suited to the representation of ontological knowledge and data-to-ontology mappings in the context of ontology-based data integration. The chase is a fundamental…
The purpose of this paper is to clarify the relationship between various conditions implying essential undecidability: our main result is that there exists a theory $T$ in which all partially recursive functions are representable, yet $T$…
The Svenonius theorem describes the (first-order) definability in a structure in terms of permutations preserving the relations of elementary extensions of the structure. In the present paper we prove a version of this theorem using…
In this paper we solve the satisfiability problem of an extended fragment of set computable theory which "forces the infinity" by a fruitful use of the witness small model property and the theory of formative processes.
In this thesis, a detailed study shows that closed itemsets and minimal generators play a key role for concisely representing both frequent itemsets and association rules. These itemsets structure the search space into equivalence classes…
In pattern mining, sequential rules provide a formal framework to capture the temporal relationships and inferential dependencies between items. However, the discovery process is computationally intensive. To obtain mining results…