Related papers: Learning from Positive and Negative Examples: New …
Finite automata (FA) are a fundamental computational abstraction that is widely used in practice for various tasks in computer science, linguistics, biology, electrical engineering, and artificial intelligence. Given an input word, an FA…
Fuelled by the popularity of the transformer architecture in deep learning, several works have investigated what formal languages a transformer can learn from data. Nonetheless, existing results remain hard to compare due to methodological…
The notion of an automaton over a changing alphabet $X=(X_i)_{i\geq 1}$ is used to define and study automorphism groups of the tree $X^*$ of finite words over $X$. The concept of bi-reversibility for Mealy-type automata is extended to…
Multiple Instance Learning (MIL) is a sub-domain of classification problems with positive and negative labels and a "bag" of inputs, where the label is positive if and only if a positive element is contained within the bag, and otherwise is…
This paper studies the complexity of operations on finite automata and the complexity of their decision problems when the alphabet is unary. Let $n$ denote the maximum of the number of states of the input finite automata considered in the…
Partially ordered automata are automata where the transition relation induces a partial order on states. The expressive power of partially ordered automata is closely related to the expressivity of fragments of first-order logic on finite…
We present an algorithm for extraction of a probabilistic deterministic finite automaton (PDFA) from a given black-box language model, such as a recurrent neural network (RNN). The algorithm is a variant of the exact-learning algorithm L*,…
A fundamental question in logic and verification is the following: for which unary predicates $P_1, \ldots, P_k$ is the monadic second-order theory of $\langle \mathbb{N}; <, P_1, \ldots, P_k \rangle$ decidable? Equivalently, for which…
In his pioneering work in the field of Inductive Inference, Gold (1967) proved that a set containing all finite languages and at least one infinite language over the same fixed alphabet is not learnable in the exact sense. Within the same…
For every natural number $n$, we classify abelian groups generated by an $n$-state time-varying automaton over the binary alphabet, as well as by an $n$-state Mealy automaton over the binary alphabet.
We consider probabilistic automata on infinite words with acceptance defined by parity conditions. We consider three qualitative decision problems: (i) the positive decision problem asks whether there is a word that is accepted with…
We develop a generic reduction procedure for active learning problems. Our approach is inspired by a recent polynomial-time reduction of the exact learning problem for weighted automata over integers to that for weighted automata over…
We consider two natural problems about nondeterministic finite automata. First, given such an automaton M of n states, and a length l, does M accept a word of length l? We show that the classic problem of triangle-free graph recognition…
We investigate learning collections of languages from texts by an inductive inference machine with access to the current datum and a bounded memory in form of states. Such a bounded memory states (BMS) learner is considered successful in…
Grammatical inference consists in learning a language or a grammar from data. In this paper, we consider a number of models for inferring a non-deterministic finite automaton (NFA) with 3 sorts of states, that must accept some words, and…
The state complexity of basic operations on finite languages (considering complete DFAs) has been in studied the literature. In this paper we study the incomplete (deterministic) state and transition complexity on finite languages of…
Assumption-based Argumentation (ABA) is advocated as a unifying formalism for various forms of non-monotonic reasoning, including logic programming. It allows capturing defeasible knowledge, subject to argumentative debate. While, in much…
Machine learning researchers and practitioners steadily enlarge the multitude of successful learning models. They achieve this through in-depth theoretical analyses and experiential heuristics. However, there is no known general-purpose…
We study the satisfiability problem of symbolic finite automata and decompose it into the satisfiability problem of the theory of the input characters and the monadic second-order theory of the indices of accepted words. We use our…
A process algebra is proposed, whose semantics maps a term to a nondeterministic finite automaton (NFA, for short). We prove a representability theorem: for each NFA $N$, there exists a process algebraic term $p$ such that its semantics is…