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Modern language models use a single matrix for input embedding and output projection. This couples two distinct objectives: token representation and discrimination over a vocabulary. This work introduces Leviathan, a Transformer…
While prior work established a verifier-based polynomial-time framework for NP, explicit deterministic machines for concrete NP-complete problems have remained elusive. In this paper, we construct fully specified deterministic Turing…
Proof automation is crucial to large-scale formal mathematics and software/hardware verification projects in ITPs. Sophisticated tools called hammers have been developed to provide general-purpose proof automation in ITPs such as Coq and…
Abstract interpreters are complex pieces of software: even if the abstract interpretation theory and companion algorithms are well understood, their implementations are subject to bugs, that might question the soundness of their…
We give a new theoretical solution to a leading-edge experimental challenge, namely to the verification of quantum computations in the regime of high computational complexity. Our results are given in the language of quantum interactive…
Type-preserving (or typed) compilation uses typing derivations to certify correctness properties of compilation. We have designed and implemented a type-preserving compiler for a simply-typed dialect of Prolog we call T-Prolog. The crux of…
This research idea paper proposes leveraging Large Language Models (LLMs) to enhance the productivity of Dafny developers. Although the use of verification-aware languages, such as Dafny, has increased considerably in the last decade, these…
State-machine based notations are ubiquitous in the description of component systems, particularly in the robotic domain. To ensure these systems are safe and predictable, formal verification techniques are important, and can be…
It is commonly agreed that the success of future proof assistants will rely on their ability to incorporate computations within deduction in order to mimic the mathematician when replacing the proof of a proposition P by the proof of an…
Advanced test-time computing strategies are essential for scaling reasoning models, but their effectiveness is capped by the models' poor self-evaluation. We propose a pairwise Explanatory Verifier, trained via reinforcement learning…
Recent work has shown that integrating large language models (LLMs) with theorem provers (TPs) in neuro-symbolic pipelines helps with entailment verification and proof-guided refinement of explanations for natural language inference (NLI).…
This paper presents the Pi-graphs, a visual paradigm for the modelling and verification of mobile systems. The language is a graphical variant of the Pi-calculus with iterators to express non-terminating behaviors. The operational semantics…
In some theory development tasks, a problem is satisfactorily solved once it is shown that a theorem (conjecture) is derivable from the background theory (premises). Depending on one's motivations, the details of the derivation of the…
The bisimulation proof method can be enhanced by employing `bisimulations up-to' techniques. A comprehensive theory of such enhancements has been developed for first-order (i.e., CCS-like) labelled transition systems (LTSs) and…
Most software verification tools can be classified into one of a number of established families, each of which has their own focus and strengths. For example, concrete counterexample generation in model checking, invariant inference in…
LLMs excel at reasoning, but validating their steps remains challenging. Formal verification offers a solution through mechanically checkable proofs. Interactive theorem provers (ITPs) dominate mathematical reasoning but require detailed…
Interactive program verification is characterized by iterations of unfinished proof attempts. To support the process of constructing a complete proof, many interactive program verification systems offer a proof scripting language as a…
While Large Language Models (LLMs) have demonstrated strong math reasoning abilities through Reinforcement Learning with *Verifiable Rewards* (RLVR), many advanced mathematical problems are proof-based, with no guaranteed way to determine…
These notes outline a formal method for program verification of numerical computation. It forms the basis of the software package VPC in its initial phase of development. Much of the style of presentation is in the form of notes that…
AI systems' ability to explain their reasoning is critical to their utility and trustworthiness. Deep neural networks have enabled significant progress on many challenging problems such as visual question answering (VQA). However, most of…