Related papers: Coalgebra Learning via Duality
Using the theory of coalgebra, we introduce a uniform framework for adding modalities to the language of propositional geometric logic. Models for this logic are based on coalgebras for an endofunctor on some full subcategory of the…
We propose various methods for combining or amalgamating propositional languages and deductive systems. We make heavy use of quantales and quantale modules in the wake of previous works by the present and other authors. We also describe…
Active automata learning from membership and equivalence queries is a foundational problem with numerous applications. We propose a novel variant of the active automata learning problem: actively learn finite automata using preference…
These lecture notes are intended as a supplement to Moore and Mertens' The Nature of Computation or as a standalone resource, and are available to anyone who wants to use them. Comments are welcome, and please let me know if you use these…
Cellular automata are a discrete dynamical system which models massively parallel computation. Much attention is devoted to computations with small time complexity for which the parallelism may provide further possibilities. In this paper,…
Information algebras arise from the idea that information comes in pieces which can be aggregated or combined into new pieces, that information refers to questions and that from any piece of information, the part relevant to a given…
Reaction systems are a formal model that has been introduced to investigate the interactive behaviors of biochemical reactions. Based on the formal framework of reaction systems, we propose new computing models called reaction automata that…
Probabilistic automata constitute a versatile and elegant model for concurrent probabilistic systems. They are equipped with a compositional theory supporting abstraction, enabled by weak probabilistic bisimulation serving as the reference…
This set of notes re-proves known results on weighted automata (over a field, also known as multiplicity automata). The text offers a unified view on theorems and proofs that have appeared in the literature over decades and were written in…
Cylindrical Algebraic Decomposition (CAD) is a key tool in computational algebraic geometry, best known as a procedure to enable Quantifier Elimination over real-closed fields. However, it has a worst case complexity doubly exponential in…
Understanding the structure of multiple related tasks allows for multi-task learning to improve the generalisation ability of one or all of them. However, it usually requires training each pairwise combination of tasks together in order to…
We present a new angle on solving quantified linear integer arithmetic based on combining the automata-based approach, where numbers are understood as bitvectors, with ideas from (nowadays prevalent) algebraic approaches, which work…
This paper presents a novel method that allows a machine learning algorithm following the transformation-based learning paradigm \cite{brill95:tagging} to be applied to multiple classification tasks by training jointly and simultaneously on…
Pomsets are a promising formalism for concurrent programs based on partially ordered sets. Among this class, series-parallel pomsets admit a convenient linear representation and can be recognized by simple algebraic structures known as…
Distributed automata are finite-state machines that operate on finite directed graphs. Acting as synchronous distributed algorithms, they use their input graph as a network in which identical processors communicate for a possibly infinite…
Automating the derivation of published results is a challenge, in part due to the informal use of mathematics by physicists, compared to that of mathematicians. Following demand, we describe a method for converting informal hand-written…
Despite the non-convexity of most modern machine learning parameterizations, Lagrangian duality has become a popular tool for addressing constrained learning problems. We revisit Augmented Lagrangian methods, which aim to mitigate the…
Regular languages -- the languages accepted by deterministic finite automata -- are known to be precisely the languages recognized by finite monoids. This characterization is the origin of algebraic language theory. In this paper, we…
The paper is devoted to two types of algebraic models of automata. The usual (first type) model leads to the developed decomposition theory (Krohn-Rhodes theory). We introduce another type of automata model and study how these automata are…
Relational verification encompasses information flow security, regression verification, translation validation for compilers, and more. Effective alignment of the programs and computations to be related facilitates use of simpler relational…