Related papers: Automatic Theorem Proving in Walnut
We report on the automation of a technique to prove the correctness of program transformations in higher-order program calculi which may permit recursive let-bindings as they occur in functional programming languages. A program…
We report on several scenarios of using automated theorem proving software in university education. In particular, we focus on using the Theorema system in a software-enhanced logic-course for students in computer science or artificial…
We propose Weighted Guarded Kleene Algebra with Tests (wGKAT), an uninterpreted weighted programming language equipped with branching, conditionals, and loops. We provide an operational semantics for wGKAT using a variant of weighted…
The demonstrated code-understanding capability of LLMs raises the question of whether they can be used for automated program verification, a task that demands high-level abstract reasoning about program properties that is challenging for…
Recently Dekking conjectured the form of the subword complexity function for the Fibonacci-Thue-Morse sequence. In this note we prove his conjecture by purely computational means, using the free software Walnut.
We study random words in a weighted regular language that achieve the maximal free energy using thermodynamics formalism. In particular, typical words in the language are algorithmically generated which have applications in computer…
Automated theorem provers and formal proof assistants are general reasoning systems that are in theory capable of proving arbitrarily hard theorems, thus solving arbitrary problems reducible to mathematics and logical reasoning. In…
The class of Boolean combinations of tree languages recognized by deterministic top-down tree automata (also known as deterministic root-to-frontier automata) is studied. The problem of determining for a given regular tree language whether…
NLTK, the Natural Language Toolkit, is a suite of open source program modules, tutorials and problem sets, providing ready-to-use computational linguistics courseware. NLTK covers symbolic and statistical natural language processing, and is…
We show that a special case of the Feferman-Vaught composition theorem gives rise to a natural notion of automata for finite words over an infinite alphabet, with good closure and decidability properties, as well as several logical…
We explore a natural class of semigroups that have word problem decidable by finite state automata. Among the main results are invariance of this property under change of generators, invariance under basic algebraic constructions and…
When proving invariance properties of a program, we face two problems. The first problem is related to the necessity of proving tautologies of considered assertion language, whereas the second manifests in the need of finding sufficiently…
We consider the task of automated theorem proving, a key AI task. Deep learning has shown promise for training theorem provers, but there are limited human-written theorems and proofs available for supervised learning. To address this…
Manually constructing a Wordnet is a difficult task, needing years of experts' time. As a first step to automatically construct full Wordnets, we propose approaches to generate Wordnet synsets for languages both resource-rich and…
We describe the Aligator.jl software package for automatically generating all polynomial invariants of the rich class of extended P-solvable loops with nested conditionals. Aligator.jl is written in the programming language Julia and is…
Algorithm portfolio and selection approaches have achieved remarkable improvements over single solvers. However, the implementation of such systems is often highly customised and specific to the problem domain. This makes it difficult for…
Automatic verification deals with the validation by means of computers of correctness certificates. The related tools, usually called proof assistants or interactive provers, provide an interactive environment for the creation of formal…
Topic modeling has been a widely used tool for unsupervised text analysis. However, comprehensive evaluations of a topic model remain challenging. Existing evaluation methods are either less comparable across different models (e.g.,…
Type-preserving (or typed) compilation uses typing derivations to certify correctness properties of compilation. We have designed and implemented a type-preserving compiler for a simply-typed dialect of Prolog we call T-Prolog. The crux of…
Mella is a minimalistic dependently typed programming language and interactive theorem prover implemented in Haskell. Its main purpose is to investigate the effective integration of automated theorem provers in a pure and simple setting.…