相关论文: A Verified Implementation of B+-Trees in Isabelle/…

A principled approach to the design of program verification and con- struction tools is applied to separation logic. The control flow is modelled by power series with convolution as separating conjunction. A generic construction lifts…

In systems verification we are often concerned with multiple, inter-dependent properties that a program must satisfy. To prove that a program satisfies a given property, the correctness of intermediate states of the program must be…

This paper introduces a series of methods for traversing binary decision trees using arithmetic operations. We present a suite of binary tree traversal algorithms that leverage novel representation matrices to flatten the full binary tree…

Network topology matrices are algebraic representations of graphs that are widely used in modeling and analysis of various applications including electrical circuits, communication networks and transportation systems. In this paper, we…

Bhat et al. developed an inductive compiler that computes density functions for probability spaces described by programs in a simple probabilistic functional language. In this work, we implement such a compiler for a modified version of…

We present a formalisation of finite Markov decision processes with rewards in the Isabelle theorem prover. We focus on the foundations required for dynamic programming and the use of reinforcement learning agents over such processes. In…

We present an approach for testing student learning outcomes in a course on automated reasoning using the Isabelle proof assistant. The approach allows us to test both general understanding of formal proofs in various logical proof systems…

Entailment trees have been proposed to simulate the human reasoning process of explanation generation in the context of open--domain textual question answering. However, in practice, manually constructing these explanation trees proves a…

Many facts possess symmetrical counterparts that often require a separate formal proof, depending on the nature of the involved symmetry. We introduce a method in Isabelle/HOL which produces such a symmetrical fact for the list datatype and…

This paper proposes an Interactive Inference Behavior Tree (IIBT) framework that integrates behavior trees (BTs) with active inference under the free energy principle for distributed multi-robot decision-making. The proposed IIBT node…

A logic for specification and verification is derived from the axioms of Zermelo-Fraenkel set theory. The proofs are performed using the proof assistant Isabelle. Isabelle is generic, supporting several different logics. Isabelle has the…

$\textbf{Motivation:}$ Hierarchical data structures are prevalent across several fields of research, as they represent an organised and efficient approach to study complex interconnected systems. Their significance is particularly evident…

This paper explores verification of constituent systems within the context of the Symphony tool platform for Systems of Systems (SoS). Our SoS modelling language, CML, supports various contractual specification elements, such as state…

We propose an online training procedure for a transformer-based automated theorem prover. Our approach leverages a new search algorithm, HyperTree Proof Search (HTPS), inspired by the recent success of AlphaZero. Our model learns from…

To develop trustworthy distributed systems, verification techniques and formal methods, including lightweight and practical approaches, have been employed to certify the design or implementation of security protocols. Lightweight formal…

We have developed a web-based pedagogical proof assistant, the Proof Tree Builder, that lets you apply rules upwards from the initial goal in sequent calculus and Hoare logic for a simple imperative language. We equipped our tool with a…

We present an approach for the verification of feed-forward neural networks in which all nodes have a piece-wise linear activation function. Such networks are often used in deep learning and have been shown to be hard to verify for modern…

In this paper, based on results of exact learning and test theory, we study arbitrary infinite binary information systems each of which consists of an infinite set of elements and an infinite set of two-valued functions (attributes) defined…

We show that interactive protocols between a prover and a verifier, a well-known tool of complexity theory, can be used in practice to certify the correctness of automated reasoning tools. Theoretically, interactive protocols exist for all…

Current formal verification of security protocols relies on specialized researchers and complex tools, inaccessible to protocol designers who informally evaluate their work with emulators. This paper addresses this gap by embedding symbolic…