Turing machines 

>
## Turing machine for L={a^n b^n c^n:n>=1}
Q:={q0,q1,q2,q3,q4,qf}:
Sig:={a,b,c,x,y,z}:
Gam:={a,b,c,x,y,z,\Delta}:
F:={qf}:
delta:=table():
delta[(q0,a)]:=[q1,x,'R']:
delta[(q1,a)]:=[q1,a,'R']:
delta[(q1,y)]:=[q1,y,'R']:
delta[(q1,b)]:=[q2,y,'R']:
delta[(q2,b)]:=[q2,b,'R']:
delta[(q2,z)]:=[q2,z,'R']:
delta[(q2,c)]:=[q3,z,'L']:
delta[(q3,z)]:=[q3,z,'L']:
delta[(q3,b)]:=[q3,b,'L']:
delta[(q3,y)]:=[q3,y,'L']:
delta[(q3,a)]:=[q3,a,'L']:
delta[(q3,x)]:=[q0,x,'R']:
delta[(q0,y)]:=[q4,y,'R']: ## finished all "a"s
delta[(q4,y)]:=[q4,y,'R']: ## delta(q4,b) and delta(q4,c) are NOT defined
delta[(q4,z)]:=[q4,z,'R']:
delta[(q4,\Delta)]:=[qf,\Delta,'L']:
tm2:=mkDTM1T(Q,Sig,Gam,op(delta),q0,\Delta,F,{q0,q1,q2,q3,q4});
 

 

`:=`(tm2, DTM1T({q0, qf, q1, q2, q3, q4}, {a, x, y, b, c, z}, {Delta, a, x, y, b, c, z}, TABLE([(q4, z) = [q4, z, R], (q1, b) = [q2, y, R], (q4, Delta) = [qf, Delta, L], (q3, z) = [q3, z, L], (q0, a) ...
`:=`(tm2, DTM1T({q0, qf, q1, q2, q3, q4}, {a, x, y, b, c, z}, {Delta, a, x, y, b, c, z}, TABLE([(q4, z) = [q4, z, R], (q1, b) = [q2, y, R], (q4, Delta) = [qf, Delta, L], (q3, z) = [q3, z, L], (q0, a) ...
`:=`(tm2, DTM1T({q0, qf, q1, q2, q3, q4}, {a, x, y, b, c, z}, {Delta, a, x, y, b, c, z}, TABLE([(q4, z) = [q4, z, R], (q1, b) = [q2, y, R], (q4, Delta) = [qf, Delta, L], (q3, z) = [q3, z, L], (q0, a) ...
`:=`(tm2, DTM1T({q0, qf, q1, q2, q3, q4}, {a, x, y, b, c, z}, {Delta, a, x, y, b, c, z}, TABLE([(q4, z) = [q4, z, R], (q1, b) = [q2, y, R], (q4, Delta) = [qf, Delta, L], (q3, z) = [q3, z, L], (q0, a) ...
`:=`(tm2, DTM1T({q0, qf, q1, q2, q3, q4}, {a, x, y, b, c, z}, {Delta, a, x, y, b, c, z}, TABLE([(q4, z) = [q4, z, R], (q1, b) = [q2, y, R], (q4, Delta) = [qf, Delta, L], (q3, z) = [q3, z, L], (q0, a) ...
> transitionGraph(tm2);
 

Plot_2d  

> stringVerificationDTM(tm2,[a,a,a,b,b,b,c,c,c],`walk`);walk;
 

Accepted (17.1.6.1)  

[q0, a, a, a, b, b, b, c, c, c] => [x, q1, a, a, b, b, b, c, c, c] => [x, a, q1, a, b, b, b, c, c, c] => [x, a, a, q1, b, b, b, c, c, c] => [x, a, a, y, q2, b, b, c, c, c] => [x, a, a, y, b, q2, b, c...
[q0, a, a, a, b, b, b, c, c, c] => [x, q1, a, a, b, b, b, c, c, c] => [x, a, q1, a, b, b, b, c, c, c] => [x, a, a, q1, b, b, b, c, c, c] => [x, a, a, y, q2, b, b, c, c, c] => [x, a, a, y, b, q2, b, c...
[q0, a, a, a, b, b, b, c, c, c] => [x, q1, a, a, b, b, b, c, c, c] => [x, a, q1, a, b, b, b, c, c, c] => [x, a, a, q1, b, b, b, c, c, c] => [x, a, a, y, q2, b, b, c, c, c] => [x, a, a, y, b, q2, b, c...
[q0, a, a, a, b, b, b, c, c, c] => [x, q1, a, a, b, b, b, c, c, c] => [x, a, q1, a, b, b, b, c, c, c] => [x, a, a, q1, b, b, b, c, c, c] => [x, a, a, y, q2, b, b, c, c, c] => [x, a, a, y, b, q2, b, c...
[q0, a, a, a, b, b, b, c, c, c] => [x, q1, a, a, b, b, b, c, c, c] => [x, a, q1, a, b, b, b, c, c, c] => [x, a, a, q1, b, b, b, c, c, c] => [x, a, a, y, q2, b, b, c, c, c] => [x, a, a, y, b, q2, b, c...
[q0, a, a, a, b, b, b, c, c, c] => [x, q1, a, a, b, b, b, c, c, c] => [x, a, q1, a, b, b, b, c, c, c] => [x, a, a, q1, b, b, b, c, c, c] => [x, a, a, y, q2, b, b, c, c, c] => [x, a, a, y, b, q2, b, c...
[q0, a, a, a, b, b, b, c, c, c] => [x, q1, a, a, b, b, b, c, c, c] => [x, a, q1, a, b, b, b, c, c, c] => [x, a, a, q1, b, b, b, c, c, c] => [x, a, a, y, q2, b, b, c, c, c] => [x, a, a, y, b, q2, b, c...
[q0, a, a, a, b, b, b, c, c, c] => [x, q1, a, a, b, b, b, c, c, c] => [x, a, q1, a, b, b, b, c, c, c] => [x, a, a, q1, b, b, b, c, c, c] => [x, a, a, y, q2, b, b, c, c, c] => [x, a, a, y, b, q2, b, c...
[q0, a, a, a, b, b, b, c, c, c] => [x, q1, a, a, b, b, b, c, c, c] => [x, a, q1, a, b, b, b, c, c, c] => [x, a, a, q1, b, b, b, c, c, c] => [x, a, a, y, q2, b, b, c, c, c] => [x, a, a, y, b, q2, b, c...
[q0, a, a, a, b, b, b, c, c, c] => [x, q1, a, a, b, b, b, c, c, c] => [x, a, q1, a, b, b, b, c, c, c] => [x, a, a, q1, b, b, b, c, c, c] => [x, a, a, y, q2, b, b, c, c, c] => [x, a, a, y, b, q2, b, c...
[q0, a, a, a, b, b, b, c, c, c] => [x, q1, a, a, b, b, b, c, c, c] => [x, a, q1, a, b, b, b, c, c, c] => [x, a, a, q1, b, b, b, c, c, c] => [x, a, a, y, q2, b, b, c, c, c] => [x, a, a, y, b, q2, b, c...
[q0, a, a, a, b, b, b, c, c, c] => [x, q1, a, a, b, b, b, c, c, c] => [x, a, q1, a, b, b, b, c, c, c] => [x, a, a, q1, b, b, b, c, c, c] => [x, a, a, y, q2, b, b, c, c, c] => [x, a, a, y, b, q2, b, c...
[q0, a, a, a, b, b, b, c, c, c] => [x, q1, a, a, b, b, b, c, c, c] => [x, a, q1, a, b, b, b, c, c, c] => [x, a, a, q1, b, b, b, c, c, c] => [x, a, a, y, q2, b, b, c, c, c] => [x, a, a, y, b, q2, b, c...
[q0, a, a, a, b, b, b, c, c, c] => [x, q1, a, a, b, b, b, c, c, c] => [x, a, q1, a, b, b, b, c, c, c] => [x, a, a, q1, b, b, b, c, c, c] => [x, a, a, y, q2, b, b, c, c, c] => [x, a, a, y, b, q2, b, c... (17.1.6.1)