Related papers: Proof System for Plan Verification under 0-Approxi…
Automatically generated code is gaining traction recently, owing to the prevalence of Large Language Models (LLMs). Further, the AlphaProof initiative has demonstrated the possibility of using AI for general mathematical reasoning.…
We introduce a protocol addressing the conformance test problem, which consists in determining whether a process under test conforms to a reference one. We consider a process to be characterized by the set of end-product it produces, which…
Computer algebra systems are really good at factoring polynomials, i.e. writing f as a product of irreducible factors. It is relatively easy to verify that we have a factorisation, but verifying that these factors are irreducible is a much…
As statistical analyses become more central to science, industry and society, there is a growing need to ensure correctness of their results. Approximate correctness can be verified by replicating the entire analysis, but can we verify…
We construct perfect zero-knowledge probabilistically checkable proofs (PZK-PCPs) for every language in #P. This is the first construction of a PZK-PCP for any language outside BPP. Furthermore, unlike previous constructions of…
In the field of robotics, researchers face a critical challenge in ensuring reliable and efficient task planning. Verifying high-level task plans before execution significantly reduces errors and enhance the overall performance of these…
Let $A \in \mathbb{R}^{n \times n}$ be invertible, $x \in \mathbb{R}^n$ unknown and $b =Ax $ given. We are interested in approximate solutions: vectors $y \in \mathbb{R}^n$ such that $\|Ay - b\|$ is small. We prove that for all $0<…
This thesis studies three topics in quantum computation and information: The approximability of quantum problems, quantum proof systems, and non-classical correlations in quantum systems. In the first area, we demonstrate a polynomial-time…
We present a formal proof in Lean of probably approximately correct (PAC) learnability of the concept class of decision stumps. This classic result in machine learning theory derives a bound on error probabilities for a simple type of…
Verification is one of the central tasks in circuit and system design. While simulation and emulation are widely used, complete correctness can only be ensured based on formal proof techniques. But these approaches often have very high run…
We give a purely model-theoretic characterization of the semantics of logic programs with negation-as-failure allowed in clause bodies. In our semantics the meaning of a program is, as in the classical case, the unique minimum model in a…
Weak memory models specify the semantics of concurrent programs on multi-core architectures. Reasoning techniques for weak memory models are often specialized to one fixed model and verification results are hence not transferable to other…
In previous work, summarized in this paper, we proposed an operation of parallel composition for rewriting-logic theories, allowing compositional specification of systems and reusability of components. The present paper focuses on…
Most formal methods see the correctness of a software system as a binary decision. However, proving the correctness of complex systems completely is difficult because they are composed of multiple components, usage scenarios, and…
We investigate the formal semantics of a simple imperative language that has both classical and quantum constructs. More specifically, we provide an operational semantics, a denotational semantics and two Hoare-style proof systems: an…
Applying deductive verification to formally prove that a program respects its formal specification is a very complex and time-consuming task due in particular to the lack of feedback in case of proof failures. Along with a non-compliance…
Maximum satisfiability is a canonical NP-hard optimization problem that appears empirically hard for random instances. Let us say that a Conjunctive normal form (CNF) formula consisting of $k$-clauses is $p$-satisfiable if there exists a…
The current verification flow of complex systems uses different engines synergistically: virtual prototyping, formal verification, simulation, emulation and FPGA prototyping. However, none is able to verify a complete architecture.…
Guaranteeing the correctness and factuality of language model (LM) outputs is a major open problem. In this work, we propose conformal factuality, a framework that can ensure high probability correctness guarantees for LMs by connecting…
This paper proves that several interactive proof systems are zero-knowledge against quantum attacks. This includes a few well-known classical zero-knowledge proof systems as well as quantum interactive proof systems for the complexity class…