Abstract
Fuzzy programming languages, such as the Fuzzy Arden Syntax (FAS), are used to describe behaviours which evolve in a fuzzy way and thus cannot be characterized neither by a Boolean outcome nor by a probability distribution. This paper introduces a semantics for FAS, focusing on the weighted parallel interpretation of its conditional statement. The proposed construction is based on the notion of a fuzzy multirelation which associates with each state in a program a fuzzy set of weighted possible evolutions. The latter is parametric on a residuated lattice which models the underlying semantic 'truth space'. Finally, a family of dynamic logics, equally parametric on the residuated lattice, is introduced to reason about FAS programs.

Abstract
Several classes of quantum circuits have been shown to provide a quantum computational advantage under certain assumptions. The study of ever more restricted classes of quantum circuits capable of quantum advantage is motivated by possible simplifications in experimental demonstrations. In this paper we study the efficiency of measurement-based quantum computation with a completely flat temporal ordering of measurements. We propose new constructions for the deterministic computation of arbitrary Boolean functions, drawing on correlations present in multi-qubit Greenberger, Horne, and Zeilinger (GHZ) states. We characterize the necessary measurement complexity using the Clifford hierarchy, and also generally decrease the number of qubits needed with respect to previous constructions. In particular, we identify a family of Boolean functions for which deterministic evaluation using non-adaptive MBQC is possible, featuring quantum advantage in width and number of gates with respect to classical circuits.

Abstract
The staggered model is a recent, very general variant of discrete-time quantum walks which, avoiding the use of a coin to direct the walker evolution, explores the underlying graph structure to build an evolution operator based on local unitaries induced by adjacent vertices. Optimising their implementation to increase resilience to decoherence phenomena motivates their analysis with the ZX-calculus. The whole optimisation can be seen as a graph reconfiguration process along which the original circuit is rewrote, significantly reducing the number of (expensive) gates used. The exercise identified an underlying pattern leading to an alternative, potentially more efficient evolution operator.

Abstract
This paper introduces Paraconsistent Reactive Graphs, as an extension of Reactive graphs that incorporates paraconsistency into the ground edges to address vagueness and inconsistency within dynamic systems. By assigning pairs of truth values to ground edges, this framework captures the uncertainty and contradictions stemming from incomplete or conflicting information. We explore the semantics of these graphs and provide a practical example to illustrate the proposed approach.

Abstract

Abstract
Discerning between quantum and classical correlations is of great importance. Bell polytopes are well established as a fundamental tool for such a purpose. In this paper, we extend this line of inquiry by applying resource theory within the context of network scenarios, to a Quantum Key Distribution (QKD) protocol, BBM92. To achieve this, we consider the causal structure P3 to describe the protocol, and we aim to develop useful statistical tests to assess it. Our objectives are twofold: firstly, to utilise the underlying causal structure of the QKD protocol to produce a geometrical analysis of the resulting nonconvex polytope, with a focus on the classical behaviours, and secondly to devise a test within this framework to evaluate the distance between any two behaviours within the generated polytope. This approach offers a unique perspective, linking deviations from expected behaviour directly to the quality of the quantum resource involved or the residual nonclassicality in protocol execution.