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We give short, closure-theoretic proofs for uniform bounds on the growth of symbolic powers of ideals in regular rings. The author recently proved these bounds in mixed characteristic using various versions of perfectoid/big Cohen-Macaulay…
We introduce two related notions of pattern enforcement in $(0,1)$-matrices: $Q$-forcing and strongly $Q$-forcing, which formalize distinct ways a fixed pattern $Q$ must appear within a larger matrix. A matrix is $Q$-forcing if every…
Anti-unification refers to the process of generalizing two (or more) goals into a single, more general, goal that captures some of the structure that is common to all initial goals. In general one is typically interested in computing what…
In this work, we investigate the expressiveness of the "conditional mutual information" (CMI) framework of Steinke and Zakynthinou (2020) and the prospect of using it to provide a unified framework for proving generalization bounds in the…
Deciding formulas mixing arithmetic and uninterpreted predicates is of practical interest, notably for applications in verification. Some decision procedures consist in building by structural induction an automaton that recognizes the set…
First some old as well as new results about P.I. algebras, Ore extensions, and degrees are presented. Then quantized $n\times r$ matrices as well as quantized factor algebras of $M_q(n)$ are analyzed. The latter are the quantized function…
Let $\MP_d$ denote the space of polynomials $f: \C \to \C$ of degree $d\geq 2$, modulo conjugation by $\Aut(\C)$. Using properties of polynomial trees (as introduced in [DM, math.DS/0608759]), we show that if $f_n$ is a divergent sequence…
The unification type of an equational theory is defined using a preorder on substitutions, called the instantiation preorder, whose scope is either restricted to the variables occurring in the unification problem, or unrestricted such that…
Quantum computations are expressed in general as quantum circuits, which are specified by ordered lists of quantum gates. The resulting specifications are used during the optimisation and execution of the expressed computations. However,…
We present verification protocols to gain confidence in the correct performance of the realization of an arbitrary universal quantum computation. The derivation of the protocols is based on the fact that matchgate computations, which are…
Uninorms play a prominent role both in the theory and the applications of Aggregations and Fuzzy Logic. In this paper the class of group-like uninorms is introduced and characterized. First, two variants of a general construction -- called…
We study the problem of enumerating answers of Conjunctive Queries ranked according to a given ranking function. Our main contribution is a novel algorithm with small preprocessing time, logarithmic delay, and non-trivial space usage during…
An efficient intuitionistic first-order prover integrated into Coq is useful to replay proofs found by external automated theorem provers. We propose a two-phase approach: An intuitionistic prover generates a certificate based on the matrix…
This paper discusses the formalization of proofs "by diagram chasing", a standard technique for proving properties in abelian categories. We discuss how the essence of diagram chases can be captured by a simple many-sorted first-order…
In type theories, universe hierarchies are commonly used to increase the expressive power of the theory while avoiding inconsistencies arising from size issues. There are numerous ways to specify universe hierarchies, and theories may…
We generalize the Safe Extremum Seeking algorithm to address the minimization of an unknown objective function subject to multiple unknown inequality and equality constraints, relying on recent results of gradient flow systems. These…
For performance and verification in machine learning, new methods have recently been proposed that optimise learning systems to satisfy formally expressed logical properties. Among these methods, differentiable logics (DLs) are used to…
The logic programming paradigm provides the basis for a new intensional view of higher-order notions. This view is realized primarily by employing the terms of a typed lambda calculus as representational devices and by using a richer form…
We study nominal anti-unification, which is concerned with computing least general generalizations for given terms-in-context. In general, the problem does not have a least general solution, but if the set of atoms permitted in…
The graph programming language GP 2 allows to apply sets of rule schemata (or "attributed" rules) non-deterministically. To analyse conflicts of programs statically, graphs labelled with expressions are overlayed to construct critical pairs…