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Algorithmic and data refinement are well studied topics that provide a mathematically rigorous approach to gradually introducing details in the implementation of software. Program refinements are performed in the context of some programming…
Transition Algebra (TA) is a type of infinite logic introduced to discuss rewriting systems. The natural deductive proof systems already introduced in TA satisfy completeness for countable signatures. However, it lacks compactness, making…
This paper presents $\forall$uto$\exists$val, a new approach for scaling LLM assessment in translating formal syntax -- such as first-order logic, regular expressions, etc -- to natural language (interpretation) or vice versa (compilation),…
This paper surveys the current state of the art in document automation (DA). The objective of DA is to reduce the manual effort during the generation of documents by automatically creating and integrating input from different sources and…
We develop a sound and complete equational theory for the functional quantum programming language QML. The soundness and completeness of the theory are with respect to the previously-developed denotational semantics of QML. The completeness…
We apply program verification technology to the problem of specifying and verifying automatic differentiation (AD) algorithms. We focus on define-by-run, a style of AD where the program that must be differentiated is executed and monitored…
We first partly develop a mathematical notion of stable consistency intended to reflect the actual consistency property of human beings. Then we give a generalization of the first and second G\"odel incompleteness theorem to stably…
TLA+ is a formal specification language used for designing, modeling, documenting, and verifying systems through model checking. Despite significant interest from the research community, knowledge about usage of the TLA+ ecosystem in…
The requirements engineering (RE) phase is pivotal in developing high-quality software. Integrating advanced modelling techniques with large language models (LLMs) and formal verification in a logical style can significantly enhance this…
Dynamic Topological Logic (DTL) is a multimodal system for reasoning about dynamical systems. It is defined semantically and, as such, most of the work done in the field has been model-theoretic. In particular, the problem of finding a…
Timed Automata (TA) is de facto a standard modelling formalism to represent systems when the interest is the analysis of their behaviour as time progresses. This modelling formalism is mostly used for checking whether the behaviours of a…
Automated verification of all members of a (potentially infinite) set of programs has the potential to be useful in program synthesis, as well as in verification of dynamically loaded code, concurrent code, and language properties. Existing…
UCLID5 is a tool for the multi-modal formal modeling, verification, and synthesis of systems. It enables one to tackle verification problems for heterogeneous systems such as combinations of hardware and software, or those that have…
The use of applications on computers, smartphones, and tablets has been considerably simplied thanks to interactive and dynamic graphical interfaces coupled with the mouse and touch screens. It is no longer necessary to be a computer…
We explore the relationship between Turing completeness and topological entropy of dynamical systems. We first prove that a natural class of Turing machines that we call "branching Turing machines" (which includes most of the known examples…
Verification proofs encode complete program behavior, yet we discard them after checking correctness. We present compiling by proving, a paradigm that transforms these proofs into optimized execution rules. By constructing All-Path…
Program verifiers such as Dafny automate proofs by outsourcing them to an SMT solver. This automation is not perfect, however, and the solver often requires hints in the form of assertions, creating a burden for the proof engineer. In this…
Tabular data synthesis is crucial for addressing privacy and security concerns in industries reliant on tabular data. While recent advancements adopt large language models (LLMs) for realistic tabular data generation, their long training…
Formally verifying software properties is a highly desirable but labor-intensive task. Recent work has developed methods to automate formal verification using proof assistants, such as Coq and Isabelle/HOL, e.g., by training a model to…
Every algorithm which can be executed on a computer can at least in principle be realized in hardware, i.e. by a discrete physical system. The problem is that up to now there is no programming language by which physical systems can…