Related papers: Rewriting and Well-Definedness within a Proof Syst…
Automated writing evaluation systems can improve students' writing insofar as students attend to the feedback provided and revise their essay drafts in ways aligned with such feedback. Existing research on revision of argumentative writing…
We propose a generic termination proof method for rewriting under strategies, based on an explicit induction on the termination property. Rewriting trees on ground terms are modeled by proof trees, generated by alternatively applying…
We revisit parallel-innermost term rewriting as a model of parallel computation on inductive data structures and provide a corresponding notion of runtime complexity parametric in the size of the start term. We propose automatic techniques…
GL is a verified tool for proving ACL2 theorems using Boolean methods such as BDD reasoning and satisfiability checking. In its typical operation, GL recursively traverses a term, computing a symbolic object representing the value of each…
Testing has become an indispensable activity of software development, yet writing good and relevant tests remains a quite challenging task. One well-known problem is that it often is impossible or unrealistic to test for every outcome, as…
Theory revision integrates inductive learning and background knowledge by combining training examples with a coarse domain theory to produce a more accurate theory. There are two challenges that theory revision and other theory-guided…
We consider the problem of inferring a grammar describing the output of a functional program given a grammar describing its input. Solutions to this problem are helpful for detecting bugs or proving safety properties of functional programs,…
To tackle long-context reasoning tasks without the quadratic complexity of standard attention mechanisms, approaches based on agent memory have emerged, which typically maintain a dynamically updated memory when linearly processing document…
In the area of networks, a common method to enforce a security policy expressed in a high-level language is based on an ad-hoc and manual rewriting process. We argue that it is possible to build a formal link between concrete and abstract…
Completion is one of the most studied techniques in term rewriting and fundamental to automated reasoning with equalities. In this paper we present new correctness proofs of abstract completion, both for finite and infinite runs. For the…
Codifying mathematical theories in a proof assistant or computer algebra system is a challenging task, of which the most difficult part is, counterintuitively, structuring definitions. This results in a steep learning curve for new users…
Convergent rewriting systems on algebraic structures give methods to solve decision problems, to prove coherence results, and to compute homological invariants. These methods are based on higher-dimensional extensions of the critical…
The application of automatic transformation processes during the formal development and optimization of programs can introduce encumbrances in the generated code that programmers usually (or presumably) do not write. An example is the…
A Retrieval-Augmented Generation (RAG)-based question-answering (QA) system enhances a large language model's knowledge by retrieving relevant documents based on user queries. Discrepancies between user queries and document phrasings often…
A major difficulty in developing and maintaining very large knowledge bases originates from the variety of forms in which knowledge is made available to the KB builder. The objective of this research is to bring together two complementary…
In this paper we show how string rewriting methods can be applied to give a new method of computing double cosets. Previous methods for double cosets were enumerative and thus restricted to finite examples. Our rewriting methods do not…
We present techniques to prove termination of cycle rewriting, that is, string rewriting on cycles, which are strings in which the start and end are connected. Our main technique is to transform cycle rewriting into string rewriting and…
This paper expands upon the finite state machine approach for the formal analysis of digital evidence. The proposed method may be used to support the feasibility of a given statement by testing it against a relevant system model. To achieve…
We present a prototype of an integrated reasoning environment for educational purposes. The presented tool is a fragment of a proof assistant and automated theorem prover. We describe the existing and planned functionality of the theorem…
Formal explainability guarantees the rigor of computed explanations, and so it is paramount in domains where rigor is critical, including those deemed high-risk. Unfortunately, since its inception formal explainability has been hampered by…