Related papers: Metamath Zero: The Cartesian Theorem Prover
Several paradigms for declarative problem solving start from a specification in a high-level language, which is then transformed to a low-level language, such as SAT or SMT. Often, this transformation includes a "grounding" step to remove…
This paper addresses the task of zero-shot image classification. The key contribution of the proposed approach is to control the semantic embedding of images -- one of the main ingredients of zero-shot learning -- by formulating it as a…
We present ZipLex, a verified framework for invertible linear-time lexical analysis following the longest match (maximal munch) semantics. Unlike past verified lexers that focus only on satisfying the semantics of regular expressions and…
A zero-finding technique for solving nonlinear equations more efficiently than they usually are with traditional iterative methods in which the order of convergence is improved is presented. The key idea in deriving this procedure is to…
We propose a training-free, binary verification workflow for zero-shot vision with off-the-shelf VLMs. It comprises two steps: (i) quantization, which turns the open-ended query into a multiple-choice question (MCQ) with a small, explicit…
Verification of functional correctness of control programs is an essential task for the development of space electronics; it is difficult and time-consuming and typically outweighs design and programming tasks in terms of development hours.…
We consider temporal logic verification of (possibly nonlinear) dynamical systems evolving over continuous state spaces. Our approach combines automata-based verification and the use of so-called barrier certificates. Automata-based…
The proofs first generated by automated theorem provers are far from optimal by any measure of simplicity. In this paper I describe a technique for simplifying automated proofs. Hopefully this discussion will stimulate interest in the…
DatalogMTL is an extension of Datalog with metric temporal operators that has found an increasing number of applications in recent years. Reasoning in DatalogMTL is, however, of high computational complexity, which makes reasoning in modern…
Deep learning techniques lie at the heart of several significant AI advances in recent years including object recognition and detection, image captioning, machine translation, speech recognition and synthesis, and playing the game of Go.…
Multiple sequence alignment (MSA) is a fundamental algorithm in bioinformatics. In a situation when the alignment might need to be protected while revealing the other information such the input sequences and the alignment score, zero…
Large language models (LLMs) can generate plausible code but offer limited guarantees of correctness. Formally verifying that implementations satisfy specifications requires constructing machine-checkable proofs, a task that remains beyond…
In order to work with mathematical content in computer systems, it is necessary to represent it in formal languages. Ideally, these are supported by tools that verify the correctness of the content, allow computing with it, and produce…
Techniques for the efficient successive under-approximation of the greatest fixpoint in TCTL formulas can be useful in fast refutation of inevitability properties and vacuity checking. We first give an integrated algorithmic framework for…
{log} (read 'setlog') was born as a Constraint Logic Programming (CLP) language where sets and binary relations are first-class citizens, thus fostering set programming. Internally, {log} is a constraint satisfiability solver implementing…
Proof assistants are getting more widespread use in research and industry to provide certified and independently checkable guarantees about theories, designs, systems and implementations. However, proof assistant implementations themselves…
Model checking and automated theorem proving are two pillars of formal methods. This paper investigates model checking from an automated theorem proving perspective, aiming at combining the expressiveness of automated theorem proving and…
We present FIMO, an innovative dataset comprising formal mathematical problem statements sourced from the International Mathematical Olympiad (IMO) Shortlisted Problems. Designed to facilitate advanced automated theorem proving at the IMO…
Large language models (LLMs) have recently demonstrated remarkable progress in formal theorem proving. Yet their ability to serve as practical assistants for mathematicians, filling in missing steps within complex proofs, remains…
Efficient zero-knowledge proofs (ZKPs) have been restricted to NP statements so far, whereas they exist for all statements in PSPACE. This work presents the first practical zero-knowledge (ZK) protocols for PSPACE-complete statements by…