Related papers: Safe, Fast, Concurrent Proof Checking for the lamb…
While slow-thinking large language models (LLMs) exhibit reflection-like reasoning, commonly referred to as the "aha moment:, their ability to generate informative critiques and refine prior solutions remains limited. In this paper, we…
Proof certificates can be used to validate the correctness of algebraic derivations. However, in practice, we frequently observed that the exact same proof steps are repeated for different sets of variables, which leads to unnecessarily…
As transistor counts in a single chip exceed tens of billions, the complexity of RTL-level simulation and verification has grown exponentially, often extending simulation campaigns to several months. In industry practice, RTL simulation is…
We describe a new approach to automatically repairing broken proofs in the Coq proof assistant in response to changes in types. Our approach combines a configurable proof term transformation with a decompiler from proof terms to tactic…
Teaching proofs is a crucial component of any undergraduate-level program that covers formal reasoning. We have developed a calculational reasoning format and refined it over several years of teaching a freshman-level course, "Logic and…
Large Reasoning Models (LRMs) achieve strong performance by generating long reasoning traces with reflection. Through a large-scale empirical analysis, we find that a substantial fraction of reflective steps consist of self-verification…
Generating samples from the output distribution of a quantum circuit is a ubiquitous task used as a building block of many quantum algorithms. Here we show how to accomplish this task on a noisy quantum processor lacking full-blown error…
Information-flow control mechanisms are difficult both to design and to prove correct. To reduce the time wasted on doomed proof attempts due to broken definitions, we advocate modern random testing techniques for finding counterexamples…
$\alpha$Check is a light-weight property-based testing tool built on top of $\alpha$Prolog, a logic programming language based on nominal logic. $\alpha$Prolog is particularly suited to the validation of the meta-theory of formal systems,…
Existing AI agents typically execute multi-step tasks autonomously and only allow user confirmation at the end. During execution, users have little control, making the confirm-at-end approach brittle: a single error can cascade and force a…
We present a novel propositional proof tracing format that eliminates complex processing, thus enabling efficient (formal) proof checking. The benefits of this format are demonstrated by implementing a proof checker in C, which outperforms…
Large Language Models (LLMs) often rely on test-time scaling via parallel decoding (for example, 512 samples) to boost reasoning accuracy, but this incurs substantial compute. We introduce CoRefine, a confidence-guided self-refinement…
The lambda-Pi-calculus Modulo is a variant of the lambda-calculus with dependent types where beta-conversion is extended with user-defined rewrite rules. It is an expressive logical framework and has been used to encode logics and type…
Parallel diffusion decoding can accelerate diffusion language model inference by unmasking multiple tokens per step, but aggressive parallelism often harms quality. Revocable decoding mitigates this by rechecking earlier tokens, yet we…
Achieving fault-tolerance will require a strong relationship between the hardware and the protocols used. Different approaches will therefore naturally have tailored proof-of-principle experiments to benchmark progress. Nevertheless,…
Memory safety defects pose a major threat to software reliability, enabling cyberattacks, outages, and crashes. To mitigate these risks, organizations adopt Compositional Bounded Model Checking (BMC), using unit proofs to formally verify…
Quantum computing will change the way we tackle certain problems. It promises to dramatically speed-up many chemical, financial, and machine-learning applications. However, to capitalize on those promises, complex design flows composed of…
The imposition of real-time constraints on a parallel computing environment- specifically high-performance, cluster-computing systems- introduces a variety of challenges with respect to the formal verification of the system's timing…
This paper proposes a new Linear Matrix Inequality (LMI) for static output feedback control assuming that a Linear Quadratic Regulator (LQR) has been previously designed for the system. The main idea is to use a quadratic candidate Lyapunov…
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…