Minimal DFAs for Testing Divisibility
Computational Complexity
2007-06-13 v1
Authors:
Boris Alexeev
Abstract
We present and prove a theorem answering the question "how many states does a minimal deterministic finite automaton (DFA) that recognizes the set of base-b numbers divisible by k have?"
Cite
@article{arxiv.cs/0309052,
title = {Minimal DFAs for Testing Divisibility},
author = {Boris Alexeev},
journal= {arXiv preprint arXiv:cs/0309052},
year = {2007}
}
Comments
LaTeX, 7 pages (corrected typo in new version)
Related papers
View all related →
Probability · Mathematics
The state complexity of random DFAs
Daniel Berend, Aryeh Kontorovich
2013-07-03
Formal Languages and Automata Theory · Computer Science
Can one quantum bit separate any pair of words with zero-error?
Aleksandrs Belovs, Juan Andres Montoya, Abuzer Yakaryılmaz
2016-02-26
Distributed, Parallel, and Cluster Computing · Computer Science
Finding the Minimal DFA of Very Large Finite State Automata with an Application to Token Passing Networks
Vlad Slavici, Daniel Kunkle, Gene Cooperman, Stephen Linton
2011-03-30
Formal Languages and Automata Theory · Computer Science
Deciding minimal distinguishing DFAs is NP-complete
Jan Martens
2023-06-07
Formal Languages and Automata Theory · Computer Science
On minimising automata with errors
Paweł Gawrychowski, Artur Jeż, Andreas Maletti
2011-03-01
Formal Languages and Automata Theory · Computer Science
A lower bound on the state complexity of transforming two-way nondeterministic finite automata to unambiguous finite automata
Semyon Petrov, Alexander Okhotin
2024-12-10
Formal Languages and Automata Theory · Computer Science
Probabilistic Finite Automaton Emptiness is Undecidable for a Fixed Automaton
Günter Rote
2024-12-09
Formal Languages and Automata Theory · Computer Science
DFAMiner: Mining minimal separating DFAs from labelled samples
Daniele Dell'Erba, Yong Li, Sven Schewe
2024-05-30
Formal Languages and Automata Theory · Computer Science
On the Gap Between Separating Words and Separating Their Reversals
Farzam Ebrahimnejad
2018-02-13
Formal Languages and Automata Theory · Computer Science
Optimal Hyper-Minimization
Andreas Maletti, Daniel Quernheim
2015-05-27
Formal Languages and Automata Theory · Computer Science
Asymptotic enumeration of Minimal Automata
Frederique Bassino, Julien David, Andrea Sportiello
2011-09-27
Quantum Physics · Physics
The Complexity of Probabilistic versus Quantum Finite Automata
Gatis Midrijanis
2007-05-23
Formal Languages and Automata Theory · Computer Science
Decidability of minimization of fuzzy automata
Lvzhou Li, Daowen Qiu
2013-05-21
Formal Languages and Automata Theory · Computer Science
Certifying DFA Bounds for Recognition and Separation
Orna Kupferman, Nir Lavee, Salomon Sickert
2022-01-20
Formal Languages and Automata Theory · Computer Science
Deterministic Suffix-reading Automata
R Keerthan, B Srivathsan, R Venkatesh, Sagar Verma
2024-10-31
Formal Languages and Automata Theory · Computer Science
Deterministic Suffix-reading Automata
R Keerthan, B Srivathsan, R Venkatesh, Sagar Verma
2026-05-13
Formal Languages and Automata Theory · Computer Science
State Complexity of Testing Divisibility
Emilie Charlier, Narad Rampersad, Michel Rigo, Laurent Waxweiler
2010-08-11
Formal Languages and Automata Theory · Computer Science
Nondeterministic State Complexity of Positional Addition
Galina Jirásková, Alexander Okhotin
2009-07-30
Formal Languages and Automata Theory · Computer Science
Random Deterministic Automata With One Added Transition
Arnaud Carayol, Philippe Duchon, Florent Koechlin, Cyril Nicaud
2025-02-05
Formal Languages and Automata Theory · Computer Science
Piecewise Testable Languages and Nondeterministic Automata
Tomáš Masopust
2016-09-07
Formal Languages and Automata Theory · Computer Science
On the rank of the communication matrix for deterministic two-way finite automata
Semyon Petrov, Fedor Petrov, Alexander Okhotin
2023-12-12
Formal Languages and Automata Theory · Computer Science
From regular expressions to deterministic finite automata: $2^{\frac{n}{2}+\sqrt{n}(\log n)^{\Theta(1)}}$ states are necessary and sufficient
Olga Martynova, Alexander Okhotin
2025-04-30
Formal Languages and Automata Theory · Computer Science
Separating Words from Every Start State with Horner Automata
Nicholas Tran
2023-09-07
Software Engineering · Computer Science
Efficient Decomposition Identification of Deterministic Finite Automata from Examples
Junjie Meng, Jie An, Yong Li, Andrea Turrini +3
2025-10-14
Formal Languages and Automata Theory · Computer Science
Primitivity, Uniform Minimality and State Complexity of Boolean Operations
Sylvie Davies
2018-03-28