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Based on a new coinductive characterization of continuous functions we extract certified programs for exact real number computation from constructive proofs. The extracted programs construct and combine exact real number algorithms with…
Distributed algorithms solving agreement problems like consensus or state machine replication are essential components of modern fault-tolerant distributed services. They are also notoriously hard to understand and reason about. Their…
Verifying programs that manipulate tree data structures often requires complex, ad-hoc proofs that are hard to generalize and automate. This paper introduces an automatic technique for analyzing such programs. Our approach combines automata…
Two methods for extracting detailed formal dependencies from the Coq and Mizar system are presented and compared. The methods are used for dependency extraction from two large mathematical repositories: the Coq Repository at Nijmegen and…
Privacy concerns in outsourced cloud databases have become more and more important recently and many efficient and scalable query processing methods over encrypted data have been proposed. However, there is very limited work on how to…
We present a model/executable specification of smart contract execution in Coq. Our formalization allows for inter-contract communication and generalizes existing work by allowing modelling of both depth-first execution blockchains (like…
Linked lists have long served as a valuable teaching tool in programming. However, the question arises: Are they truly practical for everyday program use? In most cases, it appears that array-based data structures offer distinct advantages,…
Although cuckoo hashing has significant applications in both theoretical and practical settings, a relevant downside is that it requires lookups to multiple locations. In many settings, where lookups are expensive, cuckoo hashing becomes a…
Capitalizing on previous encodings and formal developments about nominal calculi and type systems, we propose a weak Higher-Order Abstract Syntax formalization of the type language of pure System F<: within Coq, a proof assistant based on…
Being able to soundly estimate roundoff errors of finite-precision computations is important for many applications in embedded systems and scientific computing. Due to the discrepancy between continuous reals and discrete finite-precision…
Quantum Information Processing, which is an exciting area of research at the intersection of physics and computer science, has great potential for influencing the future development of information processing systems. The building of…
We present a set of tools for rewriting modulo associativity and commutativity (AC) in Coq, solving a long-standing practical problem. We use two building blocks: first, an extensible reflexive decision procedure for equality modulo AC;…
We advocate here the use of computational logic for systems biology, as a \emph{unified and safe} framework well suited for both modeling the dynamic behaviour of biological systems, expressing properties of them, and verifying these…
We describe the basic notions of co-induction as they are available in the coq system. As an application, we describe arithmetic properties for simple representations of real numbers.
Recent advancements in Unified Multimodal Models (UMMs) have significantly advanced text-to-image (T2I) generation, particularly through the integration of Chain-of-Thought (CoT) reasoning. However, existing CoT-based T2I methods largely…
The Lax Logical Framework, LLFP, was introduced, by a team including the last two authors, to provide a conceptual framework for integrating different proof development tools, thus allowing for external evidence and for postponing,…
Combinatorial optimization (CO) problems, central to operation research and theoretical computer science, present significant computational challenges due to their NP-hard nature. While large language models (LLMs) have emerged as promising…
A dictionary (or map) is a key-value store that requires all keys be unique, and a multimap is a key-value store that allows for multiple values to be associated with the same key. We design hashing-based indexing schemes for dictionaries…
Latent Chain-of-Thought (Latent CoT) models promise efficient reasoning via continuous representations, yet exhibit puzzling performance inconsistencies: excelling at exploration (ProsQA: 97.0%) but failing at computation (GSM8K: 34.1%). We…
The lock-free, ordered, linked list is an important, standard example of a concurrent data structure. An obvious, practical drawback of textbook implementations is that failed compare-and-swap (CAS) operations lead to retraversal of the…