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In the present work, we lay out a new theory showing that all automata can always be co-lexicographically partially ordered, and an intrinsic measure of their complexity can be defined and effectively determined, namely, the minimum width…
The classical subset construction for non-deterministic automata can be generalized to other side-effects captured by a monad. The key insight is that both the state space of the determinized automaton and its semantics---languages over an…
We present a passive automata learning algorithm that can extract automata from recurrent networks with very large or even infinite alphabets. Our method combines overapproximations from the field of Abstract Interpretation and passive…
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…
In order to successfully perform tasks specified by natural language instructions, an artificial agent operating in a visual world needs to map words, concepts, and actions from the instruction to visual elements in its environment. This…
We consider grammar-restricted exact learning of formulas and terms in finite variable logics. We propose a novel and versatile automata-theoretic technique for solving such problems. We first show results for learning formulas that…
We consider discriminative dictionary learning in a distributed online setting, where a network of agents aims to learn a common set of dictionary elements of a feature space and model parameters while sequentially receiving observations.…
We provide new insights on the determinization and minimization of tree automata using congruences on trees. From this perspective, we study a Brzozowski's style minimization algorithm for tree automata. First, we prove correct this method…
We introduce a new class of automata (which we coin EU-automata) running on infininte trees of arbitrary (finite) arity. We develop and study several algorithms to perform classical operations (union, intersection, complement, projection,…
Complementation of finite automata is a basic operation used in numerous applications. The standard way to complement a nondeterministic finite automaton (NFA) is to transform it into an equivalent deterministic finite automaton (DFA) and…
When dealing with deep neural network (DNN) applications on edge devices, continuously updating the model is important. Although updating a model with real incoming data is ideal, using all of them is not always feasible due to limits, such…
We propose DFAMiner, a passive learning tool for learning minimal separating deterministic finite automata (DFA) from a set of labelled samples. Separating automata are an interesting class of automata that occurs generally in regular model…
In this paper, we extend the notion of (word) derivatives and partial derivatives due to (respectively) Brzozowski and Antimirov to tree derivatives using already known inductive formulae of quotients. We define a new family of extended…
This is Chapter 24 in the "AutoMathA" handbook. Finite automata have been used effectively in recent years to define infinite groups. The two main lines of research have as their most representative objects the class of automatic groups…
Automata learning is a popular technique for inferring minimal automata through membership and equivalence queries. In this paper, we generalise learning to the theory of coalgebras. The approach relies on the use of logical formulas as…
We generalize some of the central results in automata theory to the abstraction level of coalgebras and thus lay out the foundations of a universal theory of automata operating on infinite objects. Let F be any set functor that preserves…
In pool-based active learning, the learner is given an unlabeled data set and aims to efficiently learn the unknown hypothesis by querying the labels of the data points. This can be formulated as the classical Optimal Decision Tree (ODT)…
In this paper we propose the Structured Deep Neural Network (structured DNN) as a structured and deep learning framework. This approach can learn to find the best structured object (such as a label sequence) given a structured input (such…
An index for a finite automaton is a powerful data structure that supports locating paths labeled with a query pattern, thus solving pattern matching on the underlying regular language. In this paper, we solve the long-standing problem of…
Deep learning based methods hold state-of-the-art results in image denoising, but remain difficult to interpret due to their construction from poorly understood building blocks such as batch-normalization, residual learning, and feature…