Related papers: Verification Protocols with Sub-Linear Communicati…
In this paper we investigate formal verification problems for Neural Network computations. Of central importance will be various robustness and minimization problems such as: Given symbolic specifications of allowed inputs and outputs in…
In this paper we present the formal, computer-supported verification of a functional implementation of Buchberger's critical-pair/completion algorithm for computing Gr\"obner bases in reduction rings. We describe how the algorithm can be…
The success of Deep Learning and its potential use in many safety-critical applications has motivated research on formal verification of Neural Network (NN) models. In this context, verification involves proving or disproving that an NN…
When large AI models are deployed as cloud-based services, clients have no guarantee that responses are correct or were produced by the intended model. Rerunning inference locally is infeasible for large models, and existing cryptographic…
A fertile area of recent research has demonstrated concrete polynomial time lower bounds for solving natural hard problems on restricted computational models. Among these problems are Satisfiability, Vertex Cover, Hamilton Path, Mod6-SAT,…
Communication is a critical part of enabling multi-agent systems to cooperate. This means that applying formal methods to protocols governing communication within multi-agent systems provides useful confidence in its reliability. In this…
Computer-aided analysis of security protocols heavily relies on equational theories to model cryptographic primitives. Most automated verifiers for security protocols focus on equational theories that satisfy the Finite Variant Property…
Reliable verification of proofs remains a bottleneck for training and evaluating AI systems on hard mathematical reasoning. Fully formal proofs, in languages like Lean, are easy to verify because they are unambiguous and modular. Most…
Univariate polynomial root-finding is both classical and important for modern computing. Frequently one seeks just the real roots of a polynomial with real coefficients. They can be approximated at a low computational cost if the polynomial…
We represent vector bundles over a regular algebraic curve as pairs of lattices over the maximal orders of its function field and we give polynomial time algorithms for several tasks: computing determinants of vector bundles, kernels and…
Communication between devices in avionics systems must be predictable and deterministic, and data must be delivered reliably. To help the system architects comply with these requirements, network protocol standards like ARINC 429 and AFDX…
We explore the power of interactive proofs with a distributed verifier. In this setting, the verifier consists of $n$ nodes and a graph $G$ that defines their communication pattern. The prover is a single entity that communicates with all…
We introduce a numerical framework to verify the finite step convergence of first-order methods for parametric convex quadratic optimization. We formulate the verification problem as a mathematical optimization problem where we maximize a…
Distributed protocols such as Paxos play an important role in many computer systems. Therefore, a bug in a distributed protocol may have tremendous effects. Accordingly, a lot of effort has been invested in verifying such protocols.…
Network protocols are programs with inputs and outputs that follow predefined communication patterns to synchronize and exchange information. There are many protocols and each serves a different purpose, e.g., routing, transport, secure…
We consider $m \times s$ matrices (with $m\geq s$) in a real affine subspace of dimension $n$. The problem of finding elements of low rank in such spaces finds many applications in information and systems theory, where low rank is…
In this paper we introduce a technique and a tool for formal verification of various quantum information processing protocols. The tool uses stabilizer formalism and is capable of representing concurrent quantum protocol, thus is more…
Verifying specifications for large-scale modern engineering systems can be a time-consuming task, as most formal verification methods are limited to systems of modest size. Recently, contract-based design and verification has been proposed…
This paper presents a new refutation procedure for multimodular systems of integer constraints that commonly arise when verifying cryptographic protocols. These systems, involving polynomial equalities and disequalities modulo different…
Different theorem provers tend to produce proof objects in different formats and this is especially the case for modal logics, where several deductive formalisms (and provers based on them) have been presented. This work falls within the…