Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
KlausSutner`Automata`Fsm`
FrontierFromDFA  |
| FrontierFromDFA[M,opts] converts DFA M | |
Details and Options
Examples
(1)
Basic Examples
(1)
A mod-counter DFA on 6 states.
In[1]:=
M=FA
;
 |  |
| ||||
In[2]:=
frw=
[M]
 | FrontierFromDFA |
Out[2]=
FrontierRW[{baab,bb,aaa,abaaab,abba,aabab,aabbaa},Alpha[2,],{{,1},{a,2},{b,3},{aa,4},{ab,5},{aab,6}}]
We can convert back to a DFA, which turns out to be isomorphic in this case.
In[3]:=
MM=
frw,
[M]
| FrontierToDFA |
 | FinalStateList |
Out[3]=
FA
|  |
| ||||
The path traced by witness in the frntier automaton.
aab
In[4]:=
HighlightGraph
MM,VertexLabelsAutomatic,
"MultiColor",EdgeStyleThick,{"","a","aa","aab"}
 | PlotFA |
 | Type |
Out[4]=
In[5]:=
 | IsomorphicQDFA |
Out[5]=
True
Forcing the frontier automaton to be periodic increases its size.
In[6]:=
frw=
[M,Method"Periodic"]
| FrontierFromDFA |
Out[6]=
FrontierRW[{bb,aaa,abba,aabbaa,baaab,babbba,aabab,abaaaab,abaab,ababa,ababbaba,baaba,baabbbaa,babaa,aabaaaaab,aabaaba,bababab,bababbbaba},Alpha[2,],{{,1},{a,2},{b,3},{aa,4},{ab,5},{ba,5},{aab,6},{aba,6},{baa,6},{bab,2},{aaba,3},{abaa,3},{abab,4},{baab,4},{baba,4},{aabaa,5},{babab,6}}]
In[7]:=
MM=
frw,
[M]
| FrontierToDFA |
| FinalStateList |
Out[7]=
FA
|  |
| ||||
In[8]:=
| PlotFA |
| Type |
Out[8]=
The machines are equivalent.
In[9]:=
| EquivalentQFA |
Out[9]=
True
 |
|
 |
|
 |
|
""