Related papers: Metamath Zero: The Cartesian Theorem Prover
Certified program synthesis (aka vericoding) is the process of automatically generating a program, its formal specification, and a machine-checkable proof of their alignment from a natural-language description. Two challenges make…
Effective versions of strong measure zero sets are developed for various levels of complexity and computability. It is shown that the sets can be equivalently defined using a generalization of supermartingales called odds supermartingales,…
In recent years, large language models (LLMs) have achieved strong performance on benchmark tasks, especially in zero or few-shot settings. However, these benchmarks often do not adequately address the challenges posed in the real-world,…
We argue that it is neither necessary nor sufficient for a mathematical proof to have epistemic value that it be "correct", in the sense of formalizable in a formal proof system. We then present a view on the relationship between…
We adapt a continuous logic axiomatization of tracial von Neumann algebras due to Farah, Hart and Sherman in order to prove a metatheorem for this class of structures in the style of proof mining, a research program that aims to obtain the…
With the wide application of machine translation, the testing of Machine Translation Systems (MTSs) has attracted much attention. Recent works apply Metamorphic Testing (MT) to address the oracle problem in MTS testing. Existing MT methods…
Formal verification provides strong guarantees of correctness of software, which are especially important in safety or security critical systems. Hoare logic is a widely used formalism for rigorous verification of software against…
Program verification is to develop the program's proof system, and to prove the proof system soundness with respect to a trusted operational semantics of the program. However, many practical program verifiers are not based on operational…
Control flow in unstructured programs can be complex and dynamic, which makes static analysis difficult. Yet, automated reasoning about unstructured control flow is important when certifying properties of binary (machine) code in…
We present ZK-SecreC, a domain-specific language for zero-knowledge proofs. We present the rationale for its design, its syntax and semantics, and demonstrate its usefulness on the basis of a number of non-trivial examples. The design…
Semantic parsers map natural language utterances into meaning representations (e.g., programs). Such models are typically bottlenecked by the paucity of training data due to the required laborious annotation efforts. Recent studies have…
Claim normalization is an integral part of any automatic fact-check verification system. It parses the typically noisy claim data, such as social media posts into normalized claims, which are then fed into downstream veracity classification…
This paper studies proofs of strong convergence of various iterative algorithms for computing the unique zeros of set-valued accretive operators that also satisfy some weak form of uniform accretivity at zero. More precisely, we extract…
We present two verification protocols where the correctness of a "target" computation is checked by means of "trap" computations that can be efficiently simulated on a classical computer. Our protocols rely on a minimal set of noise-free…
The claim matching (CM) task can benefit an automated fact-checking pipeline by putting together claims that can be resolved with the same fact-check. In this work, we are the first to explore zero-shot and few-shot learning approaches to…
We show that strategies implemented in automatic theorem proving involve an interesting tradeoff between execution speed, proving speedup/computational time and usefulness of information. We advance formal definitions for these concepts by…
Building mathematical optimization models is critical in operations research (OR), while it requires substantial human expertise. Recent advancements have utilized large language models (LLMs) to automate this modeling process. However,…
The generally accepted wisdom in computational circles is that pure proof verification is a solved problem and that the computationally hard elements and fertile areas of study lie in proof discovery. This wisdom presumably does hold for…
Runtime verification is an effective automated method for specification-based offline testing and analysis as well as online monitoring of complex systems. The specification language is often a variant of regular expressions or a popular…
In earlier work, we introduced flexible inference and decision-theoretic metareasoning to address the intractability of normative inference. Here, rather than pursuing the task of computing beliefs and actions with decision models composed…