Sample CA inputs

These examples are for use with the perl CA emulator provided at the bottom of Computability_and_Complexity/Formal_Languages/Other_Language_Classes/Counting_Languages. That page also contains a description of what a CA is and how it works.

This machine accepts strings of the form ${\displaystyle \{a^{n}b^{m}a^{n}b^{m}ccc|n,m\geq 0\}}$.

 :States:

q1a q1b q2a q2b q3 q4 q5 q6 q7

 :Counters:

m n

 :Start State:

q1a

 :Accept States:

q7

 :alphabet:

a b c

 :rules:

q1a c q5
q1a a q1b -> m++
q1b a q1a -> m++
q1a b q2b -> n++
q1b b q2b -> n++
q2a b q2b -> n++
q2b b q2a -> n++
q2a c q5 m==0
q2a a q3 m>0 -> m--
q2b a q3 m>0 -> m--
q3 a q3 m>0 -> m--
q3 b q4 m==0 n>0 -> n--
q4 b q4 n>0 -> n--
q4 c q5 n==0
q5 c q6
q6 c q7

Some sample inputs:
These accept:

a b b b a b b b c c c

c c c

a a a a c c c

These reject:

a a b b a b b c c c

a a b a a b c c

a a a c c c

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