Related papers: Completion of Choice
A partial algebra construction of Gr\"atzer and Schmidt from "Characterizations of congruence lattices of abstract algebras" (Acta Sci. Math. (Szeged) 24 (1963), 34-59) is adapted to provide an alternative proof to a well-known fact that…
Although Dynamic Epistemic Logic (DEL) is an influential logical framework for representing and reasoning about information change, little is known about the computational complexity of its associated decision problems. In fact, we only…
We study completions of Archimedean vector lattices relative to any nonempty set of positively-homogeneous functions on finite-dimensional real vector spaces. Examples of such completions include square mean closed and geometric closed…
Continuous first-order logic is used to apply model-theoretic analysis to analytic structures (e.g. Hilbert spaces, Banach spaces, probability spaces, etc.). Classical computable model theory is used to examine the algorithmic structure of…
Nondeterministic choice is a useful program construct that provides a way to describe the behaviour of a program without specifying the details of possible implementations. It supports the stepwise refinement of programs, a method that has…
A Leibniz class is a class of logics closed under the formation of term-equivalent logics, compatible expansions, and non-indexed products of sets of logics. We study the complete lattice of all Leibniz classes, called the Leibniz…
We propose a novel and efficient algorithm for the collaborative preference completion problem, which involves jointly estimating individualized rankings for a set of entities over a shared set of items, based on a limited number of…
The Kochen-Specker no-go theorem established that hidden-variable theories in quantum mechanics necessarily admit contextuality. This theorem is formally stated in terms of the partial Boolean algebra structure of projectors on a Hilbert…
We present a novel algebraic combinatorial view on low-rank matrix completion based on studying relations between a few entries with tools from algebraic geometry and matroid theory. The intrinsic locality of the approach allows for the…
We consider probabilistic automata on infinite words with acceptance defined by parity conditions. We consider three qualitative decision problems: (i) the positive decision problem asks whether there is a word that is accepted with…
Multi-valued functions are common in computable analysis (built upon the Type 2 Theory of Effectivity), and have made an appearance in complexity theory under the moniker search problems leading to complexity classes such as PPAD and PLS…
This paper considers the problem of matrix completion when some number of the columns are completely and arbitrarily corrupted, potentially by a malicious adversary. It is well-known that standard algorithms for matrix completion can return…
Incomplete pairwise comparison matrices offer a natural way of expressing preferences in decision making processes. Although ordinal information is crucial, there is a bias in the literature: cardinal models dominate. Ordinal models usually…
Due to challenging applications such as collaborative filtering, the matrix completion problem has been widely studied in the past few years. Different approaches rely on different structure assumptions on the matrix in hand. Here, we focus…
Random constraint satisfaction problems play an important role in computer science and combinatorics. For example, they provide challenging benchmark instances for algorithms and they have been harnessed in probabilistic constructions of…
We determine all composition-closed equational classes of Boolean functions. These classes provide a natural generalization of clones and iterative algebras: they are closed under composition, permutation and identification…
A lot of research activity has recently taken place around the chase procedure, due to its usefulness in data integration, data exchange, query optimization, peer data exchange and data correspondence, to mention a few. As the chase has…
Fundamentally, every static program analyser searches for a proof through a combination of heuristics providing candidate solutions and a candidate validation technique. Essentially, the heuristic reduces a second-order problem to a…
We investigate the topological aspects of some algebraic computation models, in particular the BSS-model. Our results can be seen as bounds on how different BSS-computability and computability in the sense of computable analysis can be. The…
We explore various combinatorial problems mostly borrowed from physics, that share the property of being continuously or discretely integrable, a feature that guarantees the existence of conservation laws that often make the problems…