Related papers: Interactive Proof Presentations with Cobra
We offer a simple graphical representation for proofs of intuitionistic logic, which is inspired by proof nets and interaction nets (two formalisms originating in linear logic). This graphical calculus of proofs inherits good features from…
Verification of neural networks is currently a hot topic in automated theorem proving. Progress has been rapid and there are now a wide range of tools available that can verify properties of networks with hundreds of thousands of nodes. In…
Quantum Computing promises accelerated simulation of certain classes of problems, in particular in plasma physics. Given the nascent interest in applying quantum computing techniques to study plasma systems, a compendium of the relevant…
The widely held belief that BQP strictly contains BPP raises fundamental questions: if we cannot efficiently compute predictions for the behavior of quantum systems, how can we test their behavior? In other words, is quantum mechanics…
In recent years we have explored using Haskell alongside a traditional mathematical formalism in our large-enrolment university course on topics including logic and formal languages, aiming to offer our students a programming perspective on…
Data analytics often involves hypothetical reasoning: repeatedly modifying the data and observing the induced effect on the computation result of a data-centric application. Recent work has proposed to leverage ideas from data provenance…
We propose a logic of interactive proofs as a framework for an intuitionistic foundation for interactive computation, which we construct via an interactive analog of the Goedel-McKinsey-Tarski-Artemov definition of Intuitionistic Logic as…
Interactive proofs (IP) model a world where a verifier delegates computation to an untrustworthy prover, verifying the prover's claims before accepting them. IP protocols have applications in areas such as verifiable computation…
Theorem proving is a fundamental aspect of mathematics, spanning from informal reasoning in natural language to rigorous derivations in formal systems. In recent years, the advancement of deep learning, especially the emergence of large…
In this dissertation we collect some results about "interactive realizability", a realizability semantics that extends the Brouwer-Heyting-Kolmogorov interpretation to (sub-)classical logic, more precisely to first-order intuitionistic…
Interactive computational environments can help students explore algorithmic concepts through collaborative hands-on experimentation. However, static and instructor controlled demos in lectures limit engagement. Even when interactive…
The need for formal definition of the very basis of mathematics arose in the last century. The scale and complexity of mathematics, along with discovered paradoxes, revealed the danger of accumulating errors across theories. Although,…
In this work, we present a visualisation tool that is able to process Coq proof scripts and generate a table representation of the contained proofs as $\LaTeX$ or PDF files. This tool has the aim to support both education and review…
We introduce pseudo-deterministic interactive proofs (psdAM): interactive proof systems for search problems where the verifier is guaranteed with high probability to output the same output on different executions. As in the case with…
There are several ways to formally represent families of data, such as lambda terms, in a type theory such as the dependent type theory of Coq. Mathematical representations are very compact ones and usually rely on the use of dependent…
Multi Prover Interactive Proof systems (MIPs)were first presented in a cryptographic context, but ever since they were used in various fields. Understanding the power of MIPs in the quantum context raises many open problems, as there are…
Verifying the truthfulness of claims usually requires joint multi-modal reasoning over both textual and visual evidence, such as analyzing both textual caption and chart image for claim verification. In addition, to make the reasoning…
One important approach to software verification is interactive theorem proving. However, writing formal proofs often requires substantial human effort, making proof automation highly important. Traditionally, proof automation has relied on…
We present Proof-of-Perception (PoP), a tool-using framework that casts multimodal reasoning as an executable graph with explicit reliability guarantees. Each perception or logic node outputs a conformal set, yielding calibrated, stepwise…
We propose to extend the Dafny system with an interactive proof mode. We present a motivating example, how the IPM works, including the main design choices we make, and a prototype implementation.