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Recent years have witnessed a hot wave of deep neural networks in various domains; however, it is not yet well understood theoretically. A theoretical characterization of deep neural networks should point out their approximation ability and…

We exhibit an algorithm to compute the strongest algebraic (or polynomial) invariants that hold at each location of a given unguarded linear hybrid automaton (i.e., a hybrid automaton having only unguarded transitions, all of whose…

This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…

In this paper, we propose an incremental abstraction method for dynamically over-approximating nonlinear systems in a bounded domain by solving a sequence of linear programs, resulting in a sequence of affine upper and lower hyperplanes…

Invariant sets define regions of the state space where system constraints are always satisfied. The majority of numerical techniques for computing invariant sets have been developed for discrete-time systems with a fixed sampling time.…

Domain generalization aims to learn knowledge invariant across different distributions while semantically meaningful for downstream tasks from multiple source domains, to improve the model's generalization ability on unseen target domains.…

We present algorithms to compute approximations of invariant measures and its attractors for IFS and GIFS, using the deterministic algorithm in a tractable way, with code optimization strategies and use of data structures and search…

We study invariant local expansion operators for conflict-free and admissible sets in Abstract Argumentation Frameworks (AFs). Such operators are directly applied on AFs, and are invariant with respect to a chosen "semantics" (that is…

The abstraction of dynamical systems is a powerful tool that enables the design of feedback controllers using a correct-by-design framework. We investigate a novel scheme to obtain data-driven abstractions of discrete-time stochastic…

We introduce the notion of porous invariants for multipath (or branching/nondeterministic) affine loops over the integers; these invariants are not necessarily convex, and can in fact contain infinitely many 'holes'. Nevertheless, we show…

Prediction models trained under the source distribution do not generalize well to a different target distribution. A valid inference about an unseen data distribution must be anchored by the invariance of certain causal mechanisms that…

This paper introduces a compositional framework for constructing finite abstractions of nonlinear interconnected impulsive systems using dissipativity-based conditions. Central to our approach is the concept of "alternating simulation…

When causal quantities cannot be point identified, researchers often pursue partial identification to quantify the range of possible values. However, the peculiarities of applied research conditions can make this analytically intractable.…

To model Web services handling data from an infinite domain, or with multiple sessions, we introduce fresh-variable automata, a simple extension of finite-state automata in which some transitions are labeled with variables that can be…

We describe a representation and a set of inference methods that combine logic programming techniques with probabilistic network representations for uncertainty (influence diagrams). The techniques emphasize the dynamic construction and…

The capacity to transfer knowledge across scientific domains relies on shared organizational principles. However, existing transfer-learning methodologies often fail to bridge radically heterogeneous systems, particularly under severe data…

This paper is concerned with a compositional approach for constructing infinite abstractions of interconnected discrete-time stochastic control systems. The proposed approach uses the interconnection matrix and joint dissipativity-type…

A classical approach to formal policy synthesis in stochastic dynamical systems is to construct a finite-state abstraction, often represented as a Markov decision process (MDP). The correctness of these approaches hinges on a behavioural…

Hybrid automata are a natural framework for modeling and analyzing systems which exhibit a mixed discrete continuous behaviour. However, the standard operational semantics defined over such models implicitly assume perfect knowledge of the…

This paper is concerned with a compositional approach for constructing abstractions of interconnected discrete-time stochastic control systems. The abstraction framework is based on new notions of so-called stochastic simulation functions,…