This paper presents the Reasoning-based, Explainable and Adaptive Contextual Tool for Smart Energy Management (REACTS). The tool enables the automatic management of energy resources in smart buildings, promoting transparent decision-making to foster user trust and support sustainability goals. It integrates Artificial Intelligence (AI) techniques, including machine learning models such as Multilayer Perceptrons, Random Forests, K-nearest Neighbors, and Support Vector Machines, to forecast energy usage and classify contextual states. Reinforcement Learning is employed to dynamically select and update forecasting models based on their historical performance. Semantic reasoning is used to represent domain knowledge through ontologies and rule-based inference, enabling context-aware decisions that adapt to user preferences and environmental conditions. Control actions are computed periodically using real-time sensor data enriched with semantic annotations. To ensure interpretability, REACTS employs Explainable AI methods, specifically SHapley Additive exPlanations, to generate feature-attribution-based justifications tailored to user profiles in both visual and textual formats. The system also incorporates green computing strategies, triggering model retraining only when performance degradation is detected, and scheduling updates during periods of lower energy or computational demand. REACTS is deployed in a real office building, operating continuously and demonstrating how contextual reasoning and explainability can enhance the reliability and sustainability of smart energy systems.

Abstract Stochastic games are a well established model for multi-agent sequential decision making under uncertainty. In practical applications, though, agents often have only partial observability of their environment. Furthermore, agents increasingly perceive their environment using data-driven approaches such as neural networks trained on continuous data. We propose the model of neuro-symbolic partially-observable stochastic games (NS-POSGs), a variant of continuous-space concurrent stochastic games that explicitly incorporates neural perception mechanisms. We focus on a one-sided setting with a partially-informed agent using discrete, data-driven observations and another, fully-informed agent. We present a new method, called one-sided NS-HSVI, for approximate solution of one-sided NS-POSGs, which exploits the piecewise constant structure of the model. Using neural network pre-image analysis to construct finite polyhedral representations and particle-based representations for beliefs, we implement our approach and illustrate its practical applicability to the analysis of pedestrian-vehicle and pursuit-evasion scenarios.

Neuro-symbolic approaches to artificial intelligence, which combine neural networks with classical symbolic techniques, are growing in prominence, necessitating formal approaches to reason about their correctness. We propose a novel modelling formalism called neuro-symbolic concurrent stochastic games (NS-CSGs), which comprise two probabilistic finite-state agents interacting in a shared continuous-state environment. Each agent observes the environment using a neural perception mechanism, which converts inputs such as images into symbolic percepts, and makes decisions symbolically. We focus on the class of NS-CSGs with Borel state spaces and prove the existence and measurability of the value function for zero-sum discounted cumulative rewards under piecewise-constant restrictions. To compute values and synthesise strategies, we first introduce a Borel measurable piecewise-constant (B-PWC) representation of value functions and propose a B-PWC value iteration. Second, we introduce two novel representations for the value functions and strategies, and propose a minimax-action-free policy iteration based on alternating player choices.

Deep neural networks can be trained to be efficient and effective controllers for dynamical systems; however, the mechanics of deep neural networks are complex and difficult to guarantee. This work presents a general approach for providing guarantees for deep neural network controllers over multiple time steps using a combination of reachability methods and open source neural network verification tools. By bounding the system dynamics and neural network outputs, the set of reachable states can be over-approximated to provide a guarantee that the system will never reach states outside the set. The method is demonstrated on the mountain car problem as well as an aircraft collision avoidance problem. Results show that this approach can provide neural network guarantees given a bounded dynamic model.

Abstract Game-theoretic techniques and equilibria analysis facilitate the design and verification of competitive systems. While algorithmic complexity of equilibria computation has been extensively studied, practical implementation and application of game-theoretic methods is more recent. Tools such as PRISM-games support automated verification and synthesis of zero-sum and ( $$\varepsilon $$ ε -optimal subgame-perfect) social welfare Nash equilibria properties for concurrent stochastic games. However, these methods become inefficient as the number of agents grows and may also generate equilibria that yield significant variations in the outcomes for individual agents. We extend the functionality of PRISM-games to support correlated equilibria, in which players can coordinate through public signals, and introduce a novel optimality criterion of social fairness, which can be applied to both Nash and correlated equilibria. We show that correlated equilibria are easier to compute, are more equitable, and can also improve joint outcomes. We implement algorithms for both normal form games and the more complex case of multi-player concurrent stochastic games with temporal logic specifications. On a range of case studies, we demonstrate the benefits of our methods.

We present novel techniques for neuro-symbolic concurrent stochastic games, a recently proposed modelling formalism to represent a set of probabilistic agents operating in a continuous-space environment using a combination of neural network based perception mechanisms and traditional symbolic methods. To date, only zero-sum variants of the model were studied, which is too restrictive when agents have distinct objectives. We formalise notions of equilibria for these models and present algorithms to synthesise them. Focusing on the finite-horizon setting, and (global) social welfare subgame-perfect optimality, we consider two distinct types: Nash equilibria and correlated equilibria. We first show that an exact solution based on backward induction may yield arbitrarily bad equilibria. We then propose an approximation algorithm called frozen subgame improvement, which proceeds through iterative solution of nonlinear programs. We develop a prototype implementation and demonstrate the benefits of our approach on two case studies: an automated car-parking system and an aircraft collision avoidance system.

Abstract Automated verification techniques for stochastic games allow formal reasoning about systems that feature competitive or collaborative behaviour among rational agents in uncertain or probabilistic settings. Existing tools and techniques focus on turn-based games, where each state of the game is controlled by a single player, and on zero-sum properties, where two players or coalitions have directly opposing objectives. In this paper, we present automated verification techniques for concurrent stochastic games (CSGs), which provide a more natural model of concurrent decision making and interaction. We also consider (social welfare) Nash equilibria, to formally identify scenarios where two players or coalitions with distinct goals can collaborate to optimise their joint performance. We propose an extension of the temporal logic rPATL for specifying quantitative properties in this setting and present corresponding algorithms for verification and strategy synthesis for a variant of stopping games. For finite-horizon properties the computation is exact, while for infinite-horizon it is approximate using value iteration. For zero-sum properties it requires solving matrix games via linear programming, and for equilibria-based properties we find social welfare or social cost Nash equilibria of bimatrix games via the method of labelled polytopes through an SMT encoding. We implement this approach in PRISM-games, which required extending the tool’s modelling language for CSGs, and apply it to case studies from domains including robotics, computer security and computer networks, explicitly demonstrating the benefits of both CSGs and equilibria-based properties.

We present a major new release of the PRISM-games model checker, featuring multiple significant advances in its support for verification and strategy synthesis of stochastic games. Firstly, concurrent stochastic games bring more realistic modelling of agents interacting in a concurrent fashion. Secondly, equilibria-based properties provide a means to analyse games in which competing or collaborating players are driven by distinct objectives. Thirdly, a real-time extension of (turn-based) stochastic games facilitates verification and strategy synthesis for systems where timing is a crucial aspect. This paper describes the advances made in the tool’s modelling language, property specification language and model checking engines in order to implement this new functionality. We also summarise the performance and scalability of the tool, and describe a selection of case studies, ranging from security protocols to robot coordination, which highlight the benefits of the new features.

Observability is mandatory for debugging purposes in all microelectronic systems. Mixed signal cores, in particular, require high observability in order to allow post production debug and to drive the design enhancements towards the real non-ideal behaviour monitored in individual modules. Controllability is also a major advantage in the design-for-debug process. This work presents a low cost controllability and observability methodology that is evaluated in terms of area cost and bandwidth capability for different operating conditions. The proposed methodology is used to add debugging capability to a DCDC, a charge pump, a LDO and a bandgap of a power management unit.