Question

L = { w | w ∈ {a, b}* and a(w) != b(w) }.

Implement the pushdown automaton A in python

Answer 1

Pushdown Automata that accepts the given language is as follows:

2 λλ baZZ abbaZZ

Above PDA is implemented below:

CODE:

def PDA(string):
    Stack = ['Z']

    for s in string:
        TOS = Stack[-1]

        if (s == 'a' or s == 'b') and TOS == 'Z':
            Stack.append(s)
        
        if (s == 'a' and TOS == 'a') or (s == 'b' and TOS == 'b'):
            Stack.append(s)
    
        if (s == 'a' and TOS == 'b') or (s == 'b' and TOS == 'a'):
            Stack.pop()     
        
    if Stack == ['Z']:
        return 'REJECTED'
    else:
        return 'ACCEPTED'
        
        
s1 = 'ababab'
s2 = 'baba'
s3 = 'abbba'
s4 = 'abbbbbbbbbbaaaaaa'
print(s1,":",PDA(s1))
print(s2,":",PDA(s2))
print(s3,":",PDA(s3))
print(s4,":",PDA(s4))

OUTPUT:

def PDA (string): stack = [,2] for s in string: TOS stack[-1] = Stack.append(s) if (s == 'a, and TOS . a.) or (s- , b. and TOS == 'b' ): Stack.append (s) if (s-, a' and TOS Stack.pop () . b.) or (s-, b. and TOS "a"): if Stack-- ['Z']: return 'REJECTED else: return'ACCEPTED" s1ababab s2baba s3abbba s4abbbbbbbbbbaaaaaa" print (s1,": " PDA(s1)) print (s2,": " PDA (s2)) print (s3,": ", PDA (s3)) print (s4,": " PDA (s4)) ababab REJECTED baba: REJECTED abbba ACCEPTED abbbbbbbbbbaaaaaa ACCEPTED