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One of the most fundamental problems in computational learning theory is the the problem of learning a finite automaton $A$ consistent with a finite set $P$ of positive examples and with a finite set $N$ of negative examples. By…

Formal Languages and Automata Theory · Computer Science 2022-06-22 Jonas Lingg , Mateus de Oliveira Oliveira , Petra Wolf

A classical problem in grammatical inference is to identify a deterministic finite automaton (DFA) from a set of positive and negative examples. In this paper, we address the related - yet seemingly novel - problem of identifying a set of…

Machine Learning · Computer Science 2017-06-07 Alexis Linard , Rick Smetsers , Frits Vaandrager , Umar Waqas , Joost van Pinxten , Sicco Verwer

The identification of a deterministic finite automaton (DFA) from labeled examples is a well-studied problem in the literature; however, prior work focuses on the identification of monolithic DFAs. Although monolithic DFAs provide accurate…

Formal Languages and Automata Theory · Computer Science 2022-05-27 Niklas Lauffer , Beyazit Yalcinkaya , Marcell Vazquez-Chanlatte , Ameesh Shah , Sanjit A. Seshia

The RPNI algorithm (Oncina, Garcia 1992) constructs deterministic finite automata from finite sets of negative and positive example words. We propose and analyze an extension of this algorithm to deterministic $\omega$-automata with…

Formal Languages and Automata Theory · Computer Science 2021-08-10 León Bohn , Christof Löding

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*,…

Machine Learning · Computer Science 2020-01-01 Gail Weiss , Yoav Goldberg , Eran Yahav

Expert demonstrations have proven an easy way to indirectly specify complex tasks. Recent algorithms even support extracting unambiguous formal specifications, e.g. deterministic finite automata (DFA), from demonstrations. Unfortunately,…

Machine Learning · Computer Science 2025-06-24 Marcell Vazquez-Chanlatte , Karim Elmaaroufi , Stefan J. Witwicki , Matei Zaharia , Sanjit A. Seshia

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…

Machine Learning · Computer Science 2025-08-25 Simon Lutz , Daniil Kaminskyi , Florian Wittbold , Simon Dierl , Falk Howar , Barbara König , Emmanuel Müller , Daniel Neider

In this work, we introduce DeepDFA, a novel approach to identifying Deterministic Finite Automata (DFAs) from traces, harnessing a differentiable yet discrete model. Inspired by both the probabilistic relaxation of DFAs and Recurrent Neural…

Machine Learning · Computer Science 2024-08-19 Elena Umili , Roberto Capobianco

The problem of k-minimisation for a DFA M is the computation of a smallest DFA N (where the size |M| of a DFA M is the size of the domain of the transition function) such that their recognized languages differ only on words of length less…

Formal Languages and Automata Theory · Computer Science 2011-03-01 Paweł Gawrychowski , Artur Jeż , Andreas Maletti

#NFA refers to the problem of counting the words of length $n$ accepted by a non-deterministic finite automaton. #NFA is #P-hard, and although fully-polynomial-time randomized approximation schemes (FPRAS) exist, they are all impractical.…

Data Structures and Algorithms · Computer Science 2025-07-01 Kuldeep S. Meel , Alexis de Colnet

It is well known that computing a minimum DFA consistent with a given set of positive and negative examples is NP-hard. Previous work has identified conditions on the input sample under which the problem becomes tractable or remains hard.…

Formal Languages and Automata Theory · Computer Science 2026-01-21 Radu Cosmin Dumitru , Ryo Yoshinaka , Ayumi Shinohara

We present a polynomial time algorithm that constructs a deterministic parity automaton (DPA) from a given set of positive and negative ultimately periodic example words. We show that this algorithm is complete for the class of…

Formal Languages and Automata Theory · Computer Science 2024-08-07 León Bohn , Christof Löding

We introduce deterministic suffix-reading automata (DSA), a new automaton model over finite words. Transitions in a DSA are labeled with words. From a state, a DSA triggers an outgoing transition on seeing a word ending with the…

Formal Languages and Automata Theory · Computer Science 2024-10-31 R Keerthan , B Srivathsan , R Venkatesh , Sagar Verma

We introduce deterministic suffix-reading automata (DSA), a new automaton model over finite words. Transitions in a DSA are labeled with words. From a state, a DSA triggers an outgoing transition on seeing a word ending with the…

Formal Languages and Automata Theory · Computer Science 2026-05-13 R Keerthan , B Srivathsan , R Venkatesh , Sagar Verma

We study the learnability of symbolic finite state automata (SFA), a model shown useful in many applications in software verification. The state-of-the-art literature on this topic follows the query learning paradigm, and so far all…

Logic in Computer Science · Computer Science 2024-02-14 Dana Fisman , Hadar Frenkel , Sandra Zilles

Specifying tasks for robotic systems traditionally requires coding expertise, deep domain knowledge, and significant time investment. While learning from demonstration offers a promising alternative, existing methods often struggle with…

Robotics · Computer Science 2024-09-12 Mattijs Baert , Sam Leroux , Pieter Simoens

Limit-average automata are weighted automata on infinite words that use average to aggregate the weights seen in infinite runs. We study approximate learning problems for limit-average automata in two settings: passive and active. In the…

Formal Languages and Automata Theory · Computer Science 2019-06-27 Jakub Michaliszyn , Jan Otop

Grammatical inference consists in learning a formal grammar as a finite state machine or as a set of rewrite rules. In this paper, we are concerned with inferring Nondeterministic Finite Automata (NFA) that must accept some words, and…

Artificial Intelligence · Computer Science 2023-03-17 Tomasz Jastrzab , Frédéric Lardeux , Eric Monfroy

The problem of learning pairwise disjoint deterministic finite automata (DFA) from positive examples has been recently addressed. In this paper, we address the problem of identifying a set of DFAs from labeled strings and come up with two…

Formal Languages and Automata Theory · Computer Science 2018-06-13 Alexis Linard

We present counting reward automata-a finite state machine variant capable of modelling any reward function expressible as a formal language. Unlike previous approaches, which are limited to the expression of tasks as regular languages, our…

Artificial Intelligence · Computer Science 2024-02-20 Tristan Bester , Benjamin Rosman , Steven James , Geraud Nangue Tasse
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