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We extend the theoretical framework of proof mining by establishing general logical metatheorems that allow for the extraction of the computational content of theorems with prima facie "non-computational" proofs from probability theory,…
Interactive proof assistants are computer programs carefully constructed to check a human-designed proof of a mathematical claim with high confidence in the implementation. However, this only validates truth of a formal claim, which may…
This article presents a relatively complete proof calculus for the dynamic logic of communicating hybrid programs dLCHP. Beyond hybrid systems, communicating hybrid programs not only feature mixed discrete and continuous dynamics but also…
The large language models (LLMs) might produce a persuasive argument within mathematical and logical fields, although such argument often includes some minor missteps, including the entire omission of side conditions, invalid inference…
Gradual verification, which supports explicitly partial specifications and verifies them with a combination of static and dynamic checks, makes verification more incremental and provides earlier feedback to developers. While an abstract,…
Switched systems are known to exhibit subtle (in)stability behaviors requiring system designers to carefully analyze the stability of closed-loop systems that arise from their proposed switching control laws. This paper presents a formal…
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…
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 (LLMs) demonstrate impressive mathematical reasoning abilities, but their solutions frequently contain errors that cannot be automatically checked. Formal theorem proving systems such as Lean 4 offer automated…
Although good encryption functions are probabilistic, most symbolic models do not capture this aspect explicitly. A typical solution, recently used to prove the soundness of such models with respect to computational ones, is to explicitly…
This paper introduces a uniform substitution calculus for $\mathsf{dL}_\text{CHP}$, the dynamic logic of communicating hybrid programs. Uniform substitution enables parsimonious prover kernels by using axioms instead of axiom schemata.…
In interactive theorem provers (ITPs), extensible syntax is not only crucial to lower the cognitive burden of manipulating complex mathematical objects, but plays a critical role in developing reusable abstractions in libraries. Most ITPs…
Formal verification provides the highest assurance of software correctness and security, but its application to large-scale, evolving systems remains a major challenge. While large language models (LLMs) have shown promise in automating…
Model checkers use automated state exploration in order to prove various properties such as reachability, non-reachability, and bisimulation over state transition systems. While model checkers have proved valuable for locating errors in…
The challenges in providing convincing arguments for safe and correct behavior of automated driving (AD) systems have so far hindered their widespread commercial deployment. Conventional development approaches such as testing and simulation…
We describe a method for building composable and extensible verification procedures within the Coq proof assistant. Unlike traditional methods that rely on run-time generation and checking of proofs, we use verified-correct procedures with…
Formal verification using interactive theorem provers ensures high-quality software. However, writing proof scripts for interactive theorem provers is labor-intensive and requires deep expertise. Recent studies have leveraged deep learning…
Quantum computing testbeds exhibit high-fidelity quantum control over small collections of qubits, enabling performance of precise, repeatable operations followed by measurements. Currently, these noisy intermediate-scale devices can…
Formal verification is increasingly recognized as a critical foundation for building reliable software systems. However, the need for specialized expertise to write precise specifications, navigate complex proof obligations, and learn…
We provide a framework consisting of tools and metatheorems for the end-to-end verification of security protocols, which bridges the gap between automated protocol verification and code-level proofs. We automatically translate a Tamarin…