Fundamental Operations in BALM - The Unknown Component Problem: Theory and Applications - page 154

The automaton is incomplete (4 states) and deterministic.
3 inputs 6 states 26 transitions
Inputs = { G0, G2, G17 }

000

011

--0

-10

010

1-0

-10
1-0

000 011

101

010_011 101

011 111 000

101

011 111

001

100_101

--0

111 101

111

101

100 111 001

101

111

001

000_001

001

Fig. 9.5 Graphical output of BALM showing the automaton S27 sup1 det.aut obtained by
determinizing the automaton S27 sup1.aut

9.5 Taking the Product of Two Automata

To illustrate the product of two automata, we consider two automata, S27Fs.aut
shown in Fig. 9.6 and S27as.aut showninFig. 9.7 . If the two automata have
different supports, the user is responsible for lifting both automata to their common
support. By an undocumented option, the product operation in BALM is defined
to automatically lift both automata to their least common support. In the example
below, the two automata start out with the same support.

product -l S27Fs.aut S27as.aut S27_prod.aut

The result is the automaton S27 prod.aut shown in Fig. 9.8 .
Note that this automaton is isomorphic to S27.aut . This is because the two
automata S27Fs.aut and S27as.aut were created by decomposing S27.aut
into two sub-automata. When their product is formed, they recreate the original
automaton. The state names of S27Fs.aut were changed from

a; b
respectively to help illustrate where the product states came from. Thus product
state

0; 1 to

b01 came from state b in S27Fs.aut and from state 01 in S27as.aut .