Related papers: A Formally Verified HOL Algebra for Dynamic Reliab…
Studies that broaden drone applications into complex tasks require a stable control framework. Recently, deep reinforcement learning (RL) algorithms have been exploited in many studies for robot control to accomplish complex tasks.…
Stability is required for real world controlled systems as it ensures that those systems can tolerate small, real world perturbations around their desired operating states. This paper shows how stability for continuous systems modeled by…
Ensuring that safety-critical applications behave as intended is an important yet challenging task. Modeling languages like differential dynamic logic (dL) have proof calculi capable of proving guarantees for such applications. However, dL…
This paper presents a novel framework for characterizing dissipativity of uncertain systems whose dynamics evolve according to differential-algebraic equations. Sufficient conditions for dissipativity (specializing to, e.g., stability or…
We present a theory of parameterized dynamic logic, namely DLp, for specifying and reasoning about a rich set of program models based on their transitional behaviours. Different from most dynamic logics that deal with regular expressions or…
This thesis introduces a formal general framework for scaling blockchain protocols by sharding. The framework is modular and it can be adjusted for different needs or sets of assumptions. We prove that sharded protocols obtained by…
Dynamic network reconfiguration is described as the process of replacing one routing function with another while the network keeps running. The main challenge is avoiding deadlock anomalies while keeping limitations on message injection and…
Deductive verification of hybrid systems (HSs) increasingly attracts more attention in recent years because of its power and scalability, where a powerful specification logic for HSs is the cornerstone. Often, HSs are naturally modelled by…
This paper presents the mechanization of a process algebra for Mobile Ad hoc Networks and Wireless Mesh Networks, and the development of a compositional framework for proving invariant properties. Mechanizing the core process algebra in…
We introduce a term algebra as a new formal specification language for the coordinating architectures of distributed systems consisting of a finite yet unbounded number of components. The language allows to describe infinite sets of systems…
We present a coalgebraic framework for studying generalisations of dynamic modal logics such as PDL and game logic in which both the propositions and the semantic structures can take values in an algebra $\mathbf{A}$ of truth-degrees. More…
Using Isabelle/HOL, we verify a union-find data structure with an explain operation due to Nieuwenhuis and Oliveras. We devise a simpler, more naive version of the explain operation whose soundness and completeness is easy to verify. Then,…
Modern verification tools for deep neural networks (DNNs) increasingly rely on abstraction to scale to realistic architectures. In parallel, proof production is becoming a critical requirement for increasing the reliability of DNN…
Deadlock detection is a challenging issue in the analysis and design of on-chip networks. We have designed an algorithm to detect deadlocks automatically in on-chip networks with wormhole switching. The algorithm has been specified and…
Higher-Order Hypergraph Learning (HOHL) was recently introduced as a principled alternative to classical hypergraph regularization, enforcing higher-order smoothness via powers of multiscale Laplacians induced by the hypergraph structure.…
Given an associative, not necessarily commutative, ring R with identity, a formal matrix calculus is introduced and developed for pairs of matrices over R. This calculus subsumes the theory of homogeneous systems of linear equations with…
DHOL is an extensional, classical logic that equips the well-known higher-order logic (HOL) with dependent types. This allows for concise encodings of important domains like size-bounded data structures, category theory, or proof theory.…
Fault Tree (FT) is a standard failure modeling technique that has been extensively used to predict reliability, availability and safety of many complex engineering systems. In order to facilitate the formal analysis of FT based analyses, a…
We present an accurate and efficient framework for real-space Hubbard-corrected density functional theory. In particular, we obtain expressions for the energy, atomic forces, and stress tensor suitable for real-space finite-difference…
We give a self-contained treatment of the theory of persistence modules indexed over the real line. We give new proofs of the standard results. Persistence diagrams are constructed using measure theory. Linear algebra lemmas are simplified…