The study of finite automata and regular languages is a privileged meeting point of algebra and logic. Since the work of Büchi, regular languages have been classified according to their descriptive complexity, i.e. the type of logical formalism required to define them. The algebraic point of view on automata is an essential complement of this classification: by providing alternative, algebraic ...

The aim of this paper is to investigate the expressibility of classical propositional monomodal logics. To this end, a notion of embedding of one logic into another is introduced, which is, roughly, a translation preserving theoremhood. This enables to measure the expressibility of a logic by a (finite or infinite) number of logics embeddable into it. This measure is calculated here for a large...

Applying quantum processors to model a high-dimensional function approximator is typical method in machine learning with potential advantage. It conjectured that the unitarity of circuits provides possible regularization avoid overfitting. However, it not clear how interplays expressibility under limitation current Noisy-Intermediate Scale Quantum devices. In this article, we perform simulation...

Parameterized quantum circuits serve as ans\"{a}tze for solving variational problems and provide a flexible paradigm programming near-term computers. Ideally, such should be highly expressive so that close approximation of the desired solution can accessed. On other hand, ansatz must also have sufficiently large gradients to allow training. Here, we derive fundamental relationship between these...

We study functional clones, which are sets of non-negative pseudo-Boolean functions closed under (essentially) multiplication, summation and limits. Functional clones naturally form a lattice under set inclusion and are closely related to counting Constraint Satisfaction Problems (CSPs). We identify a sublattice of interesting functional clones and investigate the relationships and properties o...

INTRODUCTION To evaluate meibomian gland function, changes of lacrimal tears and ocular surface parameters and tear inflammatory mediators following cataract surgery. METHODS 48 eyes of 34 patients who underwent uncomplicated phacoemulsification were involved and divided into 2 groups with those who had preexisting dry-eye before cataract surgery and those who did not. Ocular symptom score, S...

We give an AC upper bound on the complexity of rst-oder queries over (in nite) databases de ned by restricted linear constraints. This result enables us to deduce the non-expressibility of various usual queries, such as the parity of the cardinality of a set or the connectivity of a graph in rst-order logic with linear constraints.

In this paper we present an overview of the verification tool μcke. It is an implementation of a BDD-based μ-calculus model checker and uses several optimization techniques that are lifted from special purpose model checkers to the μ-calculus. This gives the user more expressibility without loosing efficiency.