Related papers: Random Wheeler Automata
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*,…
Local Fourier analysis is a commonly used tool to assess the quality and aid in the construction of geometric multigrid methods for translationally invariant operators. In this paper we automate the process of local Fourier analysis and…
The Burrows-Wheeler Transform is a string transformation that plays a fundamental role for the design of self-indexing compressed data structures. Over the years, researchers have successfully extended this transformation outside the…
Let $S$ be a string of length $n$ with characters from an alphabet of size $\sigma$. The \emph{subsequence automaton} of $S$ (often called the \emph{directed acyclic subsequence graph}) is the minimal deterministic finite automaton…
Families of deterministic finite automata (FDFA) represent regular $\omega$-languages through their ultimately periodic words (UP-words). An FDFA accepts pairs of words, where the first component corresponds to a prefix of the UP-word, and…
The communication matrix for two-way deterministic finite automata (2DFA) with $n$ states is defined for an automaton over a full alphabet of all $(2n+1)^n$ possible symbols: its rows and columns are indexed by strings, and the entry $(u,…
It is proved that every regular expression of alphabetic width $n$, that is, with $n$ occurrences of symbols of the alphabet, can be transformed into a deterministic finite automaton (DFA) with $2^{\frac{n}{2}+(\frac{\log_2…
This paper introduces Wasserstein Adversarially Regularized Graph Autoencoder (WARGA), an implicit generative algorithm that directly regularizes the latent distribution of node embedding to a target distribution via the Wasserstein metric.…
We solve the dynamic Predecessor Problem with high probability (whp) in constant time, using only $n^{1+\delta}$ bits of memory, for any constant $\delta > 0$. The input keys are random wrt a wider class of the well studied and practically…
An acyclic deterministic finite automaton (ADFA) is a data structure that represents a set of strings (i.e., a dictionary) and facilitates a pattern searching problem of determining whether a given pattern string is present in the…
Automata learning is a successful tool for many application domains such as robotics and automatic verification. Typically, automata learning techniques operate in a supervised learning setting (active or passive) where they learn a finite…
Every language recognized by a non-deterministic finite automaton can be recognized by a deterministic automaton, at the cost of a potential increase of the number of states, which in the worst case can go from $n$ states to $2^n$ states.…
Given a string $T$ on an alphabet of size $\sigma$, we describe a bidirectional Burrows-Wheeler index that takes $O(|T|\log{\sigma})$ bits of space, and that supports the addition \emph{and removal} of one character, on the left or right…
Semiautomata form a rich class of sequence-processing algorithms with applications in natural language processing, robotics, computational biology, and data mining. We establish the first Statistical Query hardness result for semiautomata…
In this paper, we present connections between three models used in different research fields: weighted finite automata~(WFA) from formal languages and linguistics, recurrent neural networks used in machine learning, and tensor networks…
A featured transition system is a transition system in which the transitions are annotated with feature expressions: Boolean expressions on a finite number of given features. Depending on its feature expression, each individual transition…
The weight maximization problem (WMP) is the problem of finding the word of highest weight on a weighted finite state automaton (WFA). It is an essential question that emerges in many optimization problems in automata theory. Unfortunately,…
In this paper, we propose a novel algorithm to learn a B\"uchi automaton from a teacher who knows an $\omega$-regular language. The algorithm is based on learning a formalism named family of DFAs (FDFAs) recently proposed by Angluin and…
We refine a uniform algebraic approach for deriving upper bounds on reset thresholds of synchronizing automata. We express the condition that an automaton is synchronizing in terms of linear algebra, and obtain upper bounds for the reset…
Traditionally, finite automata theory has been used as a framework for the representation of possibly infinite sets of strings. In this work, we introduce the notion of second-order finite automata, a formalism that combines finite automata…