Related papers: Formally Verified Approximate Policy Iteration
An important research thread in algorithmic game theory studies the design of efficient truthful mechanisms that approximate the optimal social welfare. A fundamental question is whether an \alpha-approximation algorithm translates into an…
Most existing implementations of multiple precision arithmetic demand that the user sets the precision {\em a priori}. Some libraries are said adaptable in the sense that they dynamically change the precision of each intermediate operation…
Symbolic execution is an SMT-based software verification and testing technique. Symbolic execution requires tracking performed computations during software simulation to reason about branches in the software under test. The prevailing…
Security is critical for everything relying on modern digital systems. Because almost all digital interactions are governed by the Internet and cryptographic protocols, these protocols must serve as reliable mechanisms that guarantee core…
Integer programming (IP) is an important and challenging problem. Approximate methods have shown promising performance on both effectiveness and efficiency for solving the IP problem. However, we observed that a large fraction of variables…
This paper addresses the problem of improving response times of robots implemented in the Robotic Operating System (ROS) using formal verification of computational-time feasibility. In order to verify the real time behaviour of a robot…
Verifying software correctness has always been an important and complicated task. Recently, formal proofs of critical properties of algorithms and even implementations are becoming practical. Currently, the most powerful automated proof…
Verifying mathematical proofs is difficult, but can be automated with the assistance of a computer. Autoformalization is the task of automatically translating natural language mathematics into a formal language that can be verified by a…
Formal methods (FM) are reliable but costly to apply, often requiring years of expert effort in industrial-scale projects such as seL4, especially for theorem proving. Recent advances in large language models (LLMs) have made automated…
Multiple-step lookahead policies have demonstrated high empirical competence in Reinforcement Learning, via the use of Monte Carlo Tree Search or Model Predictive Control. In a recent work \cite{efroni2018beyond}, multiple-step greedy…
Implementing a complex concept as an executable model in a strongly typed, purely functional language hits a sweet spot between mere simulation and formal specification. For research and education it is often desirable to enrich the…
With the growing popularity of Large Reasoning Models and their results in solving mathematical problems, it becomes crucial to measure their capabilities. We introduce a pipeline for both automatic and interactive verification as a more…
Informal mathematics has been central to modern large language model (LLM) reasoning, offering flexibility and enabling efficient construction of arguments. However, purely informal reasoning is prone to logical gaps and subtle errors that…
Large language models (LLM), such as Google's Minerva and OpenAI's GPT families, are becoming increasingly capable of solving mathematical quantitative reasoning problems. However, they still make unjustified logical and computational…
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…
Ensuring the safety of reinforcement learning (RL) policies in high-stakes environments requires not only formal verification but also interpretability and targeted falsification. While model checking provides formal guarantees, its…
This set of theories presents a formalisation in Isabelle/HOL+Isar of data dependencies between components. The approach allows to analyse system structure oriented towards efficient checking of system: it aims at elaborating for a concrete…
We present a new method for statistical verification of quantitative properties over a partially unknown system with actions, utilising a parameterised model (in this work, a parametric Markov decision process) and data collected from…
We provide simple equational principles for deriving rely-guarantee-style inference rules and refinement laws based on idempotent semirings. We link the algebraic layer with concrete models of programs based on languages and execution…
Reactive programs are ubiquitous in modern applications, and so verification is highly desirable. We present a verification strategy for reactive programs with a large or infinite state space utilising algebraic laws for reactive relations.…