DFA_example_multiplies_of_3.svg


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 S 0 ):
S 0 ε | 0 S 0 | 1 S 1
S 1 0 S 2 | 1 S 0
S 2 0 S 1 | 1 S 2

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:
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20 March 2007

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