Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
KlausSutner`Automata`Fsm`
ProductFA  |
| ProductFA[M1,M2] generates the product automaton for M1 M2 | |
Details and Options
Examples
(1)
Basic Examples
(1)
Automata for all words beginning respectively ending in a.
In[1]:=
M1=FA
;
 |  |
| ||||
In[2]:=
M2=FA
;
|  |
| ||||
Only the accessible part of the full product is constructed. However, states that fail to be co-accessible have to be eliminated separately. In the example, the whole left part is not co-accessible.
In[3]:=
M=
[M1,M2];
[M,TrimFalse]
 | ProductFA |
 | PlotFA |
Out[3]=
In[4]:=
| StateList |
Out[4]=
{{1,1},{2,2},{3,1},{2,1},{3,2}}
Checking the language.
In[5]:=
| LanguageFA |
Out[5]=
{{},{a},{aa},{aaa,aba},{aaaa,aaba,abaa,abba},{aaaaa,aaaba,aabaa,aabba,abaaa,ababa,abbaa,abbba}}
Other Boolean operations.
In[6]:=
M=
M1,M2,
"Union";
[M,5]
| ProductFA |
 | Type |
| LanguageFA |
Out[6]=
{{},{a},{aa,ab,ba},{aaa,aab,aba,abb,baa,bba},{aaaa,aaab,aaba,aabb,abaa,abab,abba,abbb,baaa,baba,bbaa,bbba},{aaaaa,aaaab,aaaba,aaabb,aabaa,aabab,aabba,aabbb,abaaa,abaab,ababa,ababb,abbaa,abbab,abbba,abbbb,baaaa,baaba,babaa,babba,bbaaa,bbaba,bbbaa,bbbba}}
In[7]:=
M=
M1,M2,
"Complement";
[M,5]
| ProductFA |
| Type |
| LanguageFA |
Out[7]=
{{},{},{ab},{aab,abb},{aaab,aabb,abab,abbb},{aaaab,aaabb,aabab,aabbb,abaab,ababb,abbab,abbbb}}
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""