Related papers: Limit Filters and Dependent Choice in Countable-Su…
A unitary perfect number is a positive integer n satisfying \sigma^*(n)=2n, where \sigma^* sums unitary divisors. Only five examples are known, and no sixth has been found. We revisit the Subbarao-Warren problem by keeping the seed factor…
We introduce finite support iterations of symmetric systems, and use them to provide a strongly modernized proof of David Pincus' classical result that the axiom of dependent choice is independent over ZF with the ordering principle…
The metric uncapacitated facility location problem (UFL) enjoys a special stature in approximation algorithms as a testbed for various techniques. Two generalizations of UFL are capacitated facility location (CFL) and lower-bounded facility…
For a relational structure ${\mathbb X}$ we investigate the partial order $\langle {\mathbb P} ({\mathbb X}) ,\subset \rangle$, where ${\mathbb P} ({\mathbb X}):=\{ f[X]: f\in \mathop{\rm Emb}\nolimits ({\mathbb X})\}$. Here we consider…
This paper presents a novel safety filter framework that ensures both safety and the preservation of the legacy control action within a nominal region. This modular design allows the safety filter to be integrated into the control hierarchy…
While learning-based control techniques often outperform classical controller designs, safety requirements limit the acceptance of such methods in many applications. Recent developments address this issue through so-called predictive safety…
Many problems can be specified by patterns of propositional formulae depending on a parameter, e.g. the specification of a circuit usually depends on the number of bits of its input. We define a logic whose formulae, called "iterated…
A Petri net is choice-free if any place has at most one transition in its postset (consuming its tokens) and it is (extended) free-choice (EFC) if the postsets of any two places are either equal or disjoint. Asymmetric choice (AC) extends…
We develop a formal theory of throughput in finite serial pipeline systems subject to stage multiplicative capacity perturbations, motivated by the deployment of AI tools in cybersecurity operations. A pipeline is a finite totally ordered…
The implementation of digital filters in processors based on fixed-point arithmetic can lead to problems related to the finite word-length. In particular, the processing of signals in such filters can produce overflows and unwanted noise…
Bounded policy iteration is an approach to solving infinite-horizon POMDPs that represents policies as stochastic finite-state controllers and iteratively improves a controller by adjusting the parameters of each node using linear…
Choiceless Polynomial Time (CPT) is one of the few remaining candidate logics for capturing PTIME. In this paper, we make progress towards separating CPT from polynomial time by firstly establishing a connection between the expressive power…
For $\lambda$ inaccessible, we may consider $(< \lambda)$-support iteration of some specific $(<\lambda)$-complete $\lambda^+$-c.c. forcing notion. But this fails a "preservation by restricting to a sub-sequence of the forcing, we "correct"…
This paper introduces the notion of control closure certificates to synthesize controllers for discrete-time control systems against $\omega$-regular specifications. Typical functional approaches to synthesize controllers against…
We first introduce and study two new classes of subsets in $T_0$ spaces - $\omega$-Rudin sets and $\omega$-well-filtered determined sets lying between the class of all closures of countable directed subsets and that of irreducible closed…
The aim of this paper is to present a method for computation of persistent homology that performs well at large filtration values. To this end we introduce the concept of filtered covers. We show that the persistent homology of a bounded…
We extend Choiceless Polynomial Time (CPT), the currently only remaining promising candidate in the quest for a logic capturing PTime, so that this extended logic has the following property: for every class of structures for which…
We propose a counterexample-guided inductive synthesis framework for the formal synthesis of closed-form sampled-data controllers for nonlinear systems to meet STL specifications over finite-time trajectories. Rather than stating the STL…
We give an iterative algorithm for phase estimation of a parameter theta, which is within a logarithmic factor of the Heisenberg limit. Unlike other methods, we do not need any entanglement or an extra rotation gate which can perform…
It is well known that limits can be computed by restricting along an initial functor, and that this often simplifies limit computation. We systematically study the algorithmic implications of this idea for diagrams indexed by a finite…