Related papers: Theorem Provers: One Size Fits All?
Following an early work of Dwork and Stockmeyer on interactive proof systems whose verifiers are two-way probabilistic finite automata, the authors initiated in 2004 a study on the computational power of quantum interactive proof systems…
Translating expressions between different logics and theorem provers is notoriously and often prohibitively difficult, due to the large differences between the logical foundations, the implementations of the systems, and the structure of…
Despite significant advancements in the general capability of large language models (LLMs), they continue to struggle with consistent and accurate reasoning, especially in complex tasks such as mathematical and code reasoning. One key…
Large language models (LLMs) have become capable mathematical problem-solvers, often producing correct proofs for challenging problems. However, correctness alone is not sufficient: mathematical proofs should also be clear, concise,…
The syntax of an imperative language does not mention explicitly the state, while its denotational semantics has to mention it. In this paper we present a framework for the verification in Coq of properties of programs manipulating the…
Null Hypothesis Significance Testing is the \textit{de facto} tool for assessing effectiveness differences between Information Retrieval systems. Researchers use statistical tests to check whether those differences will generalise to online…
Formally verifying system properties is one of the most effective ways of improving system quality, but its high manual effort requirements often render it prohibitively expensive. Tools that automate formal verification, by learning from…
Bibliometrics is useful to analyze the research impact for measuring the research quality. Different bibliographic databases like Scopus, Web of Science, Google Scholar etc. are accessed for evaluating the trend of publications and…
The ability to identify and control different kinds of linguistic information encoded in vector representations of words has many use cases, especially for explainability and bias removal. This is usually done via a set of simple…
Interactive-proof games model the scenario where an honest party interacts with powerful but strategic provers, to elicit from them the correct answer to a computational question. Interactive proofs are increasingly used as a framework to…
In an emerging computing paradigm, computational capabilities, from processing power to storage capacities, are offered to users over communication networks as a cloud-based service. There, demanding computations are outsourced in order to…
CoqQ is a framework for reasoning about quantum programs in the Coq proof assistant. Its main components are: a deeply embedded quantum programming language, in which classic quantum algorithms are easily expressed, and an expressive…
We investigate here a new version of the Calculus of Inductive Constructions (CIC) on which the proof assistant Coq is based: the Calculus of Congruent Inductive Constructions, which truly extends CIC by building in arbitrary first-order…
This paper describes the formal verification of two Turing machines using the program verifier Dafny. Both machines are deciders, so we prove total correctness. They are typical first examples of Turing machines used in any course of…
The evaluation of Information Retrieval (IR) systems typically uses query-document pairs with corresponding human-labelled relevance assessments (qrels). These qrels are used to determine if one system is better than another based on…
Cryptographic interactive proof systems provide an efficient and scalable means of verifying the results of computation on blockchain. A prover constructs a proof, off-chain, that the execution of a program on a given input terminates with…
While the use of formal verification techniques is well established in the development of mission-critical software, it is still rare in the production of most other kinds of software. We share our experience that a formal verification tool…
We address the challenges of scaling verification efforts to match the increasing complexity and size of systems. We propose a research agenda aimed at building a performant proof engine by studying the asymptotic performance of proof…
Theorem proving in natural mathematical language - the mixture of symbolic and natural language used by humans - plays a central role in mathematical advances and education, and tests aspects of reasoning that are core to intelligence. Yet…
E prover is a state-of-the-art theorem prover for first-order logic with equality. E prover is built around a saturation loop, where new clauses are derived by inference rules from previously derived clauses. Selection of clauses for the…