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File:DFA example multiplies of 3.svg

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    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
      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.
    In some countries this may not be legally possible; if so:
    I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.

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    inception

    20 March 2007

    media type

    image/svg+xml

    checksum

    9fd8169865e66c0aabac0fd077b62a9e4e42bc14

    determination method or standard: SHA-1

    data size

    7,258 byte

    height

    158 pixel

    width

    358 pixel

    File history

    Click on a date/time to view the file as it appeared at that time.

    Date/TimeThumbnailDimensionsUserComment
    current08:38, 4 November 2020Thumbnail for version as of 08:38, 4 November 2020358 × 158 (7 KB)Jochen Burghardtcolorize state circles
    18:31, 12 February 2018Thumbnail for version as of 18:31, 12 February 2018358 × 158 (8 KB)LeythReshaped the graph again.
    18:27, 12 February 2018Thumbnail for version as of 18:27, 12 February 2018654 × 194 (8 KB)LeythEnhancing the graph with an automata generation helper.
    16:33, 16 May 2008Thumbnail for version as of 16:33, 16 May 20081,230 × 523 (21 KB)Mormegilbottom arrows fixed
    03:08, 20 March 2007Thumbnail for version as of 03:08, 20 March 20071,230 × 523 (19 KB)MikmFixed two of the arrows
    03:05, 20 March 2007Thumbnail for version as of 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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