File:DFA example multiplies of 3.svg

Original file ‎(SVG file, nominally 358 × 158 pixels, file size: 7 KB)

Summary

Description
English: Example of a DFA that accepts binary numbers that are multiples of 3.
Čeština: Příklad deterministického konečného automatu, který přijímá binární čísla, která jsou beze zbytku dělitelná třemi.
Date
Source Own work
Author Self-made
Other versions Original PNG
Transition monoid
  ε
012
0
021
1
102
10
120
01
201
010
210
ε
012
ε
012
0
021
1
102
10
120
01
201
010
210
0
021
0
021
ε
012
01
201
010
210
1
102
10
120
1
102
1
102
10
120
ε
012
0
021
010
210
01
201
10
120
10
120
1
102
010
210
01
201
ε
012
0
021
01
201
01
201
010
210
0
021
ε
012
10
120
1
102
010
210
010
210
01
201
10
120
1
102
0
021
ε
012

Numeric entries denote functions mapping a state to a state; e.g. 102 abbreviates the function mapping state 0, 1, and 2 to state 1, 0, and 2, respectively; this is the function for digesting an input "1". The table shows the result of function composition, e.g. 021 ∘ 102 = 201, and 102 ∘ 021 = 120. Grey entries give a shortest input string corresponding to a function.

Equivalent alternate representations
Regular grammar
(Start symbol S0):
S0 ε | 0 S0 | 1 S1
S1 0 S2 | 1 S0
S2 0 S1 | 1 S2

Regular expression:

(0|(1(01*(00)*0)*1)*)*

Licensing

Public domain I, the copyright holder of this work, release this work into the public domain. This applies worldwide.
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Wikimedia username: Mikm
author name string: Self-made
URL: https://commons.wikimedia.org/wiki/user:Mikm

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copyrighted, dedicated to the public domain by copyright holder

copyright license

released into the public domain by the copyright holder

inception

20 March 2007

source of file

original creation by uploader

media type

image/svg+xml

checksum

9fd8169865e66c0aabac0fd077b62a9e4e42bc14

determination method: SHA-1

data size

7,258 byte

height

158 pixel

width

358 pixel

File history

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Date/TimeThumbnailDimensionsUserComment
current08:38, 4 November 2020358 × 158 (7 KB)Jochen Burghardtcolorize state circles
18:31, 12 February 2018358 × 158 (8 KB)LeythReshaped the graph again.
18:27, 12 February 2018654 × 194 (8 KB)LeythEnhancing the graph with an automata generation helper.
16:33, 16 May 20081,230 × 523 (21 KB)Mormegilbottom arrows fixed
03:08, 20 March 20071,230 × 523 (19 KB)MikmFixed two of the arrows
03:05, 20 March 20071,230 × 523 (19 KB)Mikm{{Information |Description= (en) Example of a DFA that accepts binary numbers that are multiplies of 3. (cs) Ukázka deterministického konečného automatu, který přijímá binární čísla, která jsou beze zbytku dělitelná třemi. |Source= Self-m
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Global file usage

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  • Usage on ar.wikipedia.org
    • أتمتة محدودة قطعية
    • مستخدم:Nojoud 95/ملعب
    • تجربة بناء طومسون
  • Usage on bg.wikipedia.org
    • Краен автомат
  • Usage on cs.wikipedia.org
    • Konečný automat
    • Wikipedie:Pod lípou/Archiv 2011/06
  • Usage on eo.wikipedia.org
    • Finia aŭtomato
  • Usage on fa.wikipedia.org
    • پذیرنده متناهی معین
    • الگوریتم ساختمان تامپسون
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    • 결정론적 유한 상태 기계
  • Usage on pl.wikipedia.org
    • Automat skończony
    • Portal:Linux
    • Portal:Linux/Portale
  • Usage on pt.wikipedia.org
    • Autômato finito determinístico
    • Algoritmo de Thompson
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    • Algoritmul lui Thompson
  • Usage on ru.wikipedia.org
    • Детерминированный конечный автомат
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    • Deterministik sonlu durum makinesi
  • Usage on uk.wikipedia.org
    • Детермінований скінченний автомат
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    • 有限狀態機

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