Are these Python programs right for defining the ambiguity of a finite grammar?

Question

I am doing Udacity CS262 and for the ambiguity detection problem. I am not sure if my decision is correct, and I am not sure if this is a formal decision.

Brief description of the problem: Write an isambig function (grammar, beginning, string) that takes the final context free grammar (encoded as a python dictionary), the grammar start character and the string. If there are two parsing trees leading to a line, then the grammar is ambiguous (or at least this is my understanding of ambiguity - please correct me if I am wrong). If the grammar is ambiguous, return True. Else return False.

Test cases:

grammar1 = [
       ("S", [ "P", ]),
       ("S", [ "a", "Q", ]) ,
       ("P", [ "a", "T"]),
       ("P", [ "c" ]),
       ("Q", [ "b" ]),
       ("T", [ "b" ]),
       ]
print isambig(grammar1, "S", ["a", "b"]) == True
print isambig(grammar1, "S", ["c"]) == False

grammar2 = [
       ("A", [ "B", ]),
       ("B", [ "C", ]),
       ("C", [ "D", ]),
       ("D", [ "E", ]),
       ("E", [ "F", ]),
       ("E", [ "G", ]),
       ("E", [ "x", "H", ]),
       ("F", [ "x", "H"]),
       ("G", [ "x", "H"]),
       ("H", [ "y", ]),
       ]
print isambig(grammar2, "A", ["x", "y"]) == True
print isambig(grammar2, "E", ["y"]) == False

grammar3 = [ # Rivers in Kenya
       ("A", [ "B", "C"]),
       ("A", [ "D", ]),
       ("B", [ "Dawa", ]),
       ("C", [ "Gucha", ]),
       ("D", [ "B", "Gucha"]),
       ("A", [ "E", "Mbagathi"]),
       ("A", [ "F", "Nairobi"]),
       ("E", [ "Tsavo" ]),
       ("F", [ "Dawa", "Gucha" ])
       ]
print isambig(grammar3, "A", ["Dawa", "Gucha"]) == True
print isambig(grammar3, "A", ["Dawa", "Gucha", "Nairobi"]) == False
print isambig(grammar3, "A", ["Tsavo"]) == False

. , , , "a b", . , .

grammar4 = [ # Simple test case
       ("S", [ "P", "Q"]),
       ("P", [ "a", ]),
       ("Q", [ "b", ]),
       ]
print isambig(grammar4, "S", ["a", "b"]) == False

:

def expand(tokens_and_derivation, grammar):
    (tokens,derivation) = tokens_and_derivation
    for token_pos in range(len(tokens)):
        for rule_index in range(len(grammar)):
            rule = grammar[rule_index]
            if tokens[token_pos] == rule[0]:
                yield ((tokens[0:token_pos] + rule[1] + tokens[token_pos+1:]), derivation + [rule_index])

def isambig(grammar, start, utterance):
    enumerated = [([start], [])]
    while True:
        new_enumerated = enumerated
        for u in enumerated:
            for i in expand(u,grammar):
                if not i in new_enumerated:
                    new_enumerated = new_enumerated + [i]

        if new_enumerated != enumerated:
            enumerated = new_enumerated
        else:
            break
    result = [xrange for xrange in enumerated if xrange[0] == utterance]
    print result
    return len(result) > 1

, :

def expand(grammar, symbol):
    result = []
    for rule in grammar:
        if rule[0] == symbol:
            result.append(rule[1])
    return result

def expand_first_nonterminal(grammar, string):
    result = []
    for i in xrange(len(string)):
        if isterminal(grammar, string[i]) == False:
            for j in expand(grammar, string[i]):
                result.append(string[:i]+j+string[i+1:])
            return result
    return None

def full_expand_string(grammar,string, result):
    for i in expand_first_nonterminal(grammar,string):
        if allterminals(grammar,i):
            result.append(i)
        else:
            full_expand_string(grammar,i,result)

def isterminal(grammar,symbol):
    for rule in grammar:
        if rule[0] == symbol:
            return False
    return True

def allterminals(grammar,string):
    for symbol in string:
        if isterminal(grammar,symbol) == False:
            return False
    return True

def returnall(grammar, start):
    result = []
    for rule in grammar:
        if rule[0] == start:
            if allterminals(grammar,rule[1]):
                return rule[1]
            else:
                full_expand_string(grammar, rule[1], result)
    return result

def isambig(grammar, start, utterance):
    count = 0
    for i in returnall(grammar,start):
        if i == utterance:
            count+=1
    if count > 1:
        return True
    else:
        return False

, , (grammar4), , , . , , .

? ?

Answer 1

, grammar4 . :

S -> PQ
P -> a
Q -> b

    S
    |
 ___|____
P        Q
|        |
a        b

, , P -> a Q -> b :

[(['a', 'b'], [0, 1, 2]), (['a', 'b'], [0, 2, 1])]

( 0,1,2 0,2,1.)

, "" , -, grammar4 .

: , , ( ), , -, .

:

grammar5 = [ 
             ("S", ["A", "B"]),
             ("S", ["B", "A"]),
             ("A", ["a"]),
             ("B", ["a"]),
           ]   
print(isambig(grammar5, "S", ["a", "a"]))

S -> AB
S -> BA
A -> a
B -> a

    S
    |
 ___|____
A        B
|        |
a        a

    S
    |
 ___|____
B        A
|        |
a        a

"" ( ).

("S", ["B", "A"]), " ", - "" , ( .)

, - ( , ) .

2: , : - .

. , ?