Related papers: Fast Automated Reasoning over String Diagrams usin…

Deterministic Finite Automata (DFAs) are of central importance in automata theory. In view of how state diagrams for DFAs are defined using directed graphs, this leads us to introduce a generalization of DFAs related to a method widely used…

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…

Automatic evaluation of essay (AES) and also called automatic essay scoring has become a severe problem due to the rise of online learning and evaluation platforms such as Coursera, Udemy, Khan academy, and so on. Researchers have recently…

This thesis proposes an advanced, generic and high-level code rewriting and analysis system in the Julia programming language, providing applied equality saturation in the presence of multiple dispatch and metaprogramming. We show how our…

Calculi of string diagrams are increasingly used to present the syntax and algebraic structure of various families of circuits, including signal flow graphs, electrical circuits and quantum processes. In many such approaches, the semantic…

We study the termination problem for probabilistic term rewrite systems. We prove that the interpretation method is sound and complete for a strengthening of positive almost sure termination, when abstract reduction systems and term rewrite…

Aligning multimodal generative models with human preferences demands reward signals that respect the compositional, multi-dimensional structure of human judgment. Prevailing RLHF approaches reduce this structure to scalar or pairwise…

Chain of Thought (CoT) was introduced in recent research as a method for improving step-by-step reasoning in Large Language Models. However, CoT has limited applications such as its need for hand-crafted few-shot exemplar prompts and no…

We deal with the problem of maintaining the suffix tree indexing structure for a fully-online collection of multiple strings, where a new character can be prepended to any string in the collection at any time. The only previously known…

A series of works has established rewriting as an essential tool in order to prove coherence properties of algebraic structures, such as MacLane's coherence theorem for monoidal categories, based on the observation that, under reasonable…

This thesis is devoted to the study of a calculus that describes the application of conditional rewriting rules and the obtained results at the same level of representation. We introduce the rewriting calculus, also called the rho-calculus,…

A foundational theory of compositional categorical rewriting theory is presented, based on a collection of fibration-like properties that collectively induce and intrinsically structure the large collection of lemmata used in the proofs of…

This paper discusses a system that accelerates reinforcement learning by using transfer from related tasks. Without such transfer, even if two tasks are very similar at some abstract level, an extensive re-learning effort is required. The…

Structural Causal Explanations (SCEs) can be used to automatically generate explanations in natural language to questions about given data that are grounded in a (possibly learned) causal model. Unfortunately they work for small data only.…

We give a procedure that can be used to automatically satisfy invariants of a certain shape. These invariants may be written with the operations intersection, composition and converse over binary relations, and equality over these…

We introduce a categorical formalism for rewriting surface-embedded graphs. Such graphs can represent string diagrams in a non-symmetric setting where we guarantee that the wires do not intersect each other. The main technical novelty is a…

This paper studies the problem of modifying the input matrix of a structured system to make the system strongly structurally controllable. We focus on the generalized structured systems that rely on zero/nonzero/arbitrary structure, i.e.,…

Many discrete optimization problems are amenable to constrained shortest-path reformulations in an extended network space, a technique that has been key in convexification, bound strengthening, and search. In this paper, we propose a…

Narrowing is a procedure that was first studied in the context of equational E-unification and that has been used in a wide range of applications. The classic completeness result due to Hullot states that any term rewriting derivation…

Multivariate polynomial dynamical systems over finite fields have been studied in several contexts, including engineering and mathematical biology. An important problem is to construct models of such systems from a partial specification of…