def test_set_new_transtable():
alphabet = ["a", "b"]
states = ["1", "2"]
table = TransitionTable(alphabet, states)
table.add_transition("a", "2", "2")
table.add_transition("b", "2", "2")
table.add_transition("a", "1", "2")
table.add_transition("b", "1", "1")
dfa = DFA(table)
# invalid table
try:
dfa.trans_table = {}
except ValueError:
pass
# new table
new_table = TransitionTable(alphabet, states)
new_table.add_transition("b", "2", "2")
new_table.add_transition("a", "1", "2")
new_table.add_transition("b", "1", "1")
dfa.trans_table = new_table
def test_set_new_transtable():
alphabet = ["a", "b"]
states = ["1", "2"]
table = TransitionTable(alphabet, states)
table.add_transition("a", "2", "2")
table.add_transition("b", "2", "2")
table.add_transition("a", "1", "2")
table.add_transition("b", "1", "1")
dfa = DFA(table)
# invalid table
try:
dfa.trans_table = {}
except ValueError:
pass
# new table
new_table = TransitionTable(alphabet, states)
new_table.add_transition("b", "2", "2")
new_table.add_transition("a", "1", "2")
new_table.add_transition("b", "1", "1")
dfa.trans_table = new_table
def test_consume():
alphabet = ["a", "b"]
states = ["1", "2"]
table = TransitionTable(alphabet, states)
table.add_transition("b", "2", "2")
table.add_transition("a", "1", "2")
table.add_transition("b", "1", "1")
dfa = DFA(table)
# accepted string
accepted = dfa.consume("ba")
assert accepted, "'ba' is expected to be accepted."
accepted = dfa.consume("babbb")
assert accepted, "'babbb' is expected to be accepted."
# not acceptable string
accepted = dfa.consume("b")
assert not accepted, "'b' is expected not to be accepted."
accepted = dfa.consume("bbb")
assert not accepted, "'bbb' is expected not to be accepted."
# dead state
accepted = dfa.consume("bbaba")
assert not accepted, "'bbaba' is expected not to be accepted."
# invalid transition
accepted = dfa.consume("babbbc")
assert not accepted, "'bac' is expected not to be accepted."
def nfa_to_dfa(self):
try:
self.alphabet.remove('ε')
except:
pass
self.new_ss = state({s.id for s in self.start_states})
temp_op = {key: set() for key in self.alphabet + ['ε']}
for ss in self.start_states:
for k, v in ss.outpaths.items():
set_v = set(v)
temp_op[k] = temp_op[k].union(set_v)
self.new_ss.outpaths = {k: list(v) for k, v in temp_op.items()}
self.new_ss.made_of = set(self.start_states)
self.states.append(self.new_ss)
self.e_transitions()
if 'ε' in self.new_ss.outpaths:
del self.new_ss.outpaths['ε']
existing_states = [self.new_ss.made_of]
new_states = [self.new_ss]
dfa_states = [self.new_ss]
while len(new_states) > 0:
next_round = []
for es in new_states:
new_dict = {key: set() for key in self.alphabet}
for sub_state in es.made_of:
for char, states in sub_state.ep_outpaths.items():
new_dict[char] = new_dict[char].union(states)
for char, states in new_dict.items():
if states not in existing_states:
id = set([s.id for s in states])
if id == set():
id = '∅'
new_state = state(id)
new_state.made_of = states
es.outpaths[char] = new_state
dfa_states.append(new_state)
existing_states.append(states)
next_round.append(new_state)
else:
for x in dfa_states:
if x.made_of == states:
es.outpaths[char] = x
break
new_states = next_round
self.my_dfa = DFA(dfa_states)
self.my_dfa.alphabet = self.alphabet
self.my_dfa.start_state = self.new_ss
acc_ids = {st.id for st in self.accept_states}
for st in self.my_dfa.states:
for s in st.made_of:
if s.id in acc_ids:
self.my_dfa.accept_states.append(st)
break
def test_consume():
alphabet = ["a", "b"]
states = ["1", "2"]
table = TransitionTable(alphabet, states)
table.add_transition("b", "2", "2")
table.add_transition("a", "1", "2")
table.add_transition("b", "1", "1")
dfa = DFA(table)
# accepted string
accepted = dfa.consume("ba")
assert accepted, "'ba' is expected to be accepted."
accepted = dfa.consume("babbb")
assert accepted, "'babbb' is expected to be accepted."
# not acceptable string
accepted = dfa.consume("b")
assert not accepted, "'b' is expected not to be accepted."
accepted = dfa.consume("bbb")
assert not accepted, "'bbb' is expected not to be accepted."
# dead state
accepted = dfa.consume("bbaba")
assert not accepted, "'bbaba' is expected not to be accepted."
# invalid transition
accepted = dfa.consume("babbbc")
assert not accepted, "'bac' is expected not to be accepted."
def test_dfa_match_bad(self):
tr = {(0, 15): 1,
(0, 22): 2,
(1, 17): 3,
(2, 17): 3,
(2, 22): 4,
(3, 22): 4,
(4, 233): 4
}
fs = {1: {'regex1'},
4: {'regex2'}
}
dfa = DFA(5, tr, 0, fs)
seq = [2]
self.assertEqual(dfa.match(seq), set(), "Matching the empty sequence should stay in the start state which is not final in this example")
tr = {(0, 15): 1,
(0, 22): 2,
(1, 17): 3,
(2, 17): 3,
(2, 22): 4,
(3, 22): 4,
(4, 233): 4
}
fs = {1: {'regex1'},
4: {'regex2'}
}
dfa = DFA(5, tr, 0, fs)
seq = [22, 22, 233, 2]
self.assertEqual(dfa.match(seq), set(), "If a transition is undefined, it must return set()")
def test_dfa_match_good1(self):
tr = {(0, 15): 1,
(0, 22): 2,
(1, 17): 3,
(2, 17): 3,
(2, 22): 4,
(3, 22): 4,
(4, 233): 4
}
fs = {1: {'regex1'},
4: {'regex2'}
}
dfa = DFA(5, tr, 0, fs)
seq = [15]
self.assertEqual(dfa.match(seq), {'regex1'}, "In this example, the sequence [15] leads into final state 1 that should return regex1 as label")
tr = {(0, 15): 1,
(0, 22): 2,
(1, 17): 3,
(2, 17): 3,
(2, 22): 4,
(3, 22): 4,
(4, 233): 4
}
fs = {1: {'regex1'},
4: {'regex2'}
}
dfa = DFA(5, tr, 0, fs)
seq = [15, 17, 22, 233]
self.assertEqual(dfa.match(seq), {'regex2'}, "In this example, the sequence [15, 17, 22, 233] leads into final state 4 that should return regex2 as label")
def setup(self):
# DFA which matches all binary strings ending in an odd number of '1's
self.dfa = DFA(**{
'states': {'q0', 'q1', 'q2'},
'symbols': {'0', '1'},
'transitions': {
'q0': {'0': 'q0', '1': 'q1'},
'q1': {'0': 'q0', '1': 'q2'},
'q2': {'0': 'q2', '1': 'q1'}
},
'initial_state': 'q0',
'final_states': {'q1'}
})
def test2():
#Example 13.1 from Automata & Computability
print('Test 2')
s0 = state(0)
s1 = state(1)
s2 = state(2)
s3 = state(3)
s0.outpaths = {'a': s1, 'b': s3}
s1.outpaths = {'a': s2, 'b': s2}
s2.outpaths = {'a': s2, 'b': s2}
s3.outpaths = {'a': s2, 'b': s2}
d = DFA([s0,s1,s2,s3])
d.start_state = s0
d.accept_states = [s1, s3]
d.alphabet = ['a', 'b']
d.minimize()
d.print_dfa(True)
"""
def subset_construction(self):
# based on:
# Subset Construction presented by Ullman (Automata course)
# extended with closure operation to work with epsilon transitions
states = 1
numeric_state = dict()
closure = self.epsilon_closure()
start = frozenset(closure[self.start])
numeric_state[start] = states - 1
finals = dict()
# empty transitions dictionary
tr = dict()
queue = collections.deque([start])
# if one of the subset states in the DFA start state is already final
fin = start & self.final.keys()
if fin:
# start state is always id 0
finals[0] = {label for q in fin for label in self.final[q]}
while queue:
# print(len(queue))
curr_state = queue.popleft()
for (a, state_set) in self.successors(curr_state).items():
# for a in range(256):
# next_state = self.next(curr_state, a)
next_state = frozenset(state_set)
if next_state:
# the state exists
if next_state not in numeric_state.keys():
states += 1
numeric_state[next_state] = states - 1
# add into queue so it gets resolved in next round
queue.append(next_state)
tr[numeric_state[curr_state],
a] = numeric_state[next_state]
fin = next_state & self.final.keys()
if fin:
finals[numeric_state[next_state]] = {
label
for q in fin for label in self.final[q]
}
# print("State Subsets", numeric_state)
return DFA(states, tr, 0, finals)
def test1():
#from https://www.gatevidyalay.com/minimization-of-dfa-minimize-dfa-example/
print('Test 1')
s0 = state(0)
s1 = state(1)
s2 = state(2)
s3 = state(3)
s4 = state(4)
s0.outpaths = {'a': s1, 'b': s2}
s1.outpaths = {'a': s1, 'b': s3}
s2.outpaths = {'a': s1, 'b': s2}
s3.outpaths = {'a': s1, 'b': s4}
s4.outpaths = {'a': s1, 'b': s2}
d = DFA([s0,s1,s2,s3,s4])
d.start_state = s1
d.accept_states = [s4]
d.alphabet = ['a', 'b']
d.minimize()
d.print_dfa(True)
"""
def test1():
#1a in HW3 in Automata & Computability
print('Test 1')
s0 = state(0)
s1 = state(1)
s0.outpaths = {'a': s1, 'b': s0}
s1.outpaths = {'a': s0, 'b': s1}
d = DFA([s0, s1])
d.start_state = s0
d.accept_states = [s0]
d.alphabet = ['a', 'b']
print(d.all_regex(False) + '\n')
def test4():
#Example 13.2 from Automata & Computability
print('Test 4')
s0 = state(0)
s1 = state(1)
s2 = state(2)
s3 = state(3)
s4 = state(4)
s5 = state(5)
s0.outpaths = {'a': s1, 'b': s2}
s1.outpaths = {'a': s3, 'b': s4}
s2.outpaths = {'a': s4, 'b': s3}
s3.outpaths = {'a': s5, 'b': s5}
s4.outpaths = {'a': s5, 'b': s5}
s5.outpaths = {'a': s5, 'b': s5}
d = DFA([s0,s1,s2,s3,s4,s5])
d.start_state = s0
d.accept_states = [s1, s2, s5]
d.alphabet = ['a', 'b']
d.minimize()
d.print_dfa(True)
"""
def test3():
#from https://www.geeksforgeeks.org/minimization-of-dfa/
print('Test 3')
s0 = state(0)
s1 = state(1)
s2 = state(2)
s3 = state(3)
s4 = state(4)
s5 = state(5)
s0.outpaths = {'0': s3, '1': s1}
s1.outpaths = {'0': s2, '1': s5}
s2.outpaths = {'0': s2, '1': s5}
s3.outpaths = {'0': s0, '1': s4}
s4.outpaths = {'0': s2, '1': s5}
s5.outpaths = {'0': s5, '1': s5}
d = DFA([s0,s1,s2,s3,s4,s5])
d.start_state = s0
d.accept_states = [s1, s2, s4]
d.alphabet = ['0', '1']
d.minimize()
d.print_dfa(True)
"""
def test5():
#accepts any variant of a(ba)*a
print('Test 5')
s0 = state(0)
s1 = state(1)
s2 = state(2)
s0.outpaths = {'a': s1}
s1.outpaths = {'a': s2, 'b': s0}
d = DFA([s0, s1, s2])
d.start_state = s0
d.accept_states = [s2]
d.alphabet = ['a', 'b']
print(d.all_regex(False))
def test3():
#1d in HW3 in Automata & Computability
print('Test 3')
s0 = state(0)
s1 = state(1)
s2 = state(2)
s3 = state(3)
s0.outpaths = {'a': s2, 'b': s1}
s1.outpaths = {'a': s3, 'b': s0}
s2.outpaths = {'a': s0, 'b': s3}
s3.outpaths = {'a': s1, 'b': s2}
d = DFA([s0, s1, s2, s3])
d.start_state = s0
d.accept_states = [s1]
d.alphabet = ['a', 'b']
print(d.all_regex() + '\n')
def test4():
#pg 17 Example 3.2 from Automata & Computability
#accepts strings w/ 3 consecutive a's
print('Test 4')
s0 = state(0)
s1 = state(1)
s2 = state(2)
s3 = state(3)
s0.outpaths = {'a': s1, 'b': s0}
s1.outpaths = {'a': s2, 'b': s0}
s2.outpaths = {'a': s3, 'b': s0}
s3.outpaths = {'a': s3, 'b': s3}
d = DFA([s0, s1, s2, s3])
d.start_state = s0
d.accept_states = [s3]
d.alphabet = ['a', 'b']
print(d.all_regex() + '\n')
def test_from_nfa_simple(self):
"""should properly convert a simple NFA to a DFA"""
nfa = NFA(**{
'states': {'q0', 'q1', 'q2'},
'symbols': {'0', '1'},
'transitions': {
'q0': {'0': {'q0', 'q1'}},
'q1': {'1': {'q2'}},
'q2': {}
},
'initial_state': 'q0',
'final_states': {'q2'}
})
dfa = DFA.from_nfa(nfa)
nose.assert_equal(dfa.states, {'{}', '{q0}', '{q0q1}', '{q2}'})
nose.assert_equal(dfa.symbols, {'0', '1'})
nose.assert_equal(dfa.transitions, {
'{}': {'0': '{}', '1': '{}'},
'{q0}': {'0': '{q0q1}', '1': '{}'},
'{q0q1}': {'0': '{q0q1}', '1': '{q2}'},
'{q2}': {'0': '{}', '1': '{}'}
})
nose.assert_equal(dfa.initial_state, '{q0}')
nose.assert_equal(dfa.final_states, {'{q2}'})
def test_dfa_match_empty(self):
tr = {(0, 15): 1,
(0, 22): 2,
(1, 17): 3,
(2, 17): 3,
(2, 22): 4,
(3, 22): 4,
(4, 233): 4
}
fs = {1: {'regex1'},
4: {'regex2'}
}
dfa = DFA(5, tr, 0, fs)
seq = []
self.assertEqual(dfa.match(seq), set(), "Matching the empty sequence should stay in the start state which is not final")
tr = {(0, 15): 0}
fs = {0: {'regex1'}}
dfa = DFA(1, tr, 0, fs)
self.assertEqual(dfa.match([]), {"regex1"}, "In this example, the start state is accepting, so the empty sequence should return the correct label")
def test6():
#Example 13.2 from Automata & Computability
#accepts {a,b} and any strings with 3+ characters
print('Test 6')
s0 = state(0)
s1 = state(1)
s2 = state(2)
s3 = state(3)
s4 = state(4)
s5 = state(5)
s0.outpaths = {'a': s1, 'b': s2}
s1.outpaths = {'a': s3, 'b': s4}
s2.outpaths = {'a': s4, 'b': s3}
s3.outpaths = {'a': s5, 'b': s5}
s4.outpaths = {'a': s5, 'b': s5}
s5.outpaths = {'a': s5, 'b': s5}
d = DFA([s0, s1, s2, s3, s4, s5])
d.start_state = s0
d.accept_states = [s1, s2, s5]
d.alphabet = ['a', 'b']
print(d.all_regex())
def create_fa(self, expression, alphabet):
new_FA = DFA()
new_FA.set_name(str(expression))
self.FA_list.append(new_FA)
self.add_tab(expression, ['FA', alphabet])
class TestDFA():
def setup(self):
# DFA which matches all binary strings ending in an odd number of '1's
self.dfa = DFA(**{
'states': {'q0', 'q1', 'q2'},
'symbols': {'0', '1'},
'transitions': {
'q0': {'0': 'q0', '1': 'q1'},
'q1': {'0': 'q0', '1': 'q2'},
'q2': {'0': 'q2', '1': 'q1'}
},
'initial_state': 'q0',
'final_states': {'q1'}
})
def test_init_json(self):
"""should copy given JSON object into new DFA"""
with open('tests/files/dfa.json', 'r') as dfa_file:
dfa_json = json.load(dfa_file)
new_dfa = DFA(**dfa_json)
nose.assert_equal(new_dfa.states, set(dfa_json['states']))
nose.assert_is_not(new_dfa.states, dfa_json['states'])
nose.assert_equal(new_dfa.symbols, set(dfa_json['symbols']))
nose.assert_is_not(new_dfa.symbols, dfa_json['symbols'])
nose.assert_equal(new_dfa.transitions, dict(dfa_json['transitions']))
nose.assert_is_not(new_dfa.transitions, dfa_json['transitions'])
nose.assert_equal(new_dfa.initial_state, dfa_json['initial_state'])
nose.assert_equal(new_dfa.final_states, set(dfa_json['final_states']))
nose.assert_is_not(new_dfa.final_states, dfa_json['final_states'])
def test_validate_automaton_missing_state(self):
"""should raise error if a state has no transitions defined"""
with nose.assert_raises(automaton.MissingStateError):
del self.dfa.transitions['q1']
self.dfa.validate_automaton()
def test_validate_automaton_missing_symbol(self):
"""should raise error if a symbol transition is missing"""
with nose.assert_raises(automaton.MissingSymbolError):
del self.dfa.transitions['q1']['1']
self.dfa.validate_automaton()
def test_validate_automaton_invalid_symbol(self):
"""should raise error if a transition references an invalid symbol"""
with nose.assert_raises(automaton.InvalidSymbolError):
self.dfa.transitions['q1']['2'] = 'q2'
self.dfa.validate_automaton()
def test_validate_automaton_invalid_state(self):
"""should raise error if a transition references an invalid state"""
with nose.assert_raises(automaton.InvalidStateError):
self.dfa.transitions['q1']['1'] = 'q3'
self.dfa.validate_automaton()
def test_validate_automaton_invalid_initial_state(self):
"""should raise error if the initial state is invalid"""
with nose.assert_raises(automaton.InvalidStateError):
self.dfa.initial_state = 'q3'
self.dfa.validate_automaton()
def test_validate_automaton_invalid_final_state(self):
"""should raise error if the final state is invalid"""
with nose.assert_raises(automaton.InvalidStateError):
self.dfa.final_states = {'q3'}
self.dfa.validate_automaton()
def test_validate_input_valid(self):
"""should return correct stop state when valid DFA input is given"""
nose.assert_equal(self.dfa.validate_input('0111'), 'q1')
def test_validate_input_invalid_symbol(self):
"""should raise error if an invalid symbol is read"""
with nose.assert_raises(automaton.InvalidSymbolError):
self.dfa.validate_input('01112')
def test_validate_input_nonfinal_state(self):
"""should raise error if the stop state is not a final state"""
with nose.assert_raises(automaton.FinalStateError):
self.dfa.validate_input('011')
def test_from_nfa_simple(self):
"""should properly convert a simple NFA to a DFA"""
nfa = NFA(**{
'states': {'q0', 'q1', 'q2'},
'symbols': {'0', '1'},
'transitions': {
'q0': {'0': {'q0', 'q1'}},
'q1': {'1': {'q2'}},
'q2': {}
},
'initial_state': 'q0',
'final_states': {'q2'}
})
dfa = DFA.from_nfa(nfa)
nose.assert_equal(dfa.states, {'{}', '{q0}', '{q0q1}', '{q2}'})
nose.assert_equal(dfa.symbols, {'0', '1'})
nose.assert_equal(dfa.transitions, {
'{}': {'0': '{}', '1': '{}'},
'{q0}': {'0': '{q0q1}', '1': '{}'},
'{q0q1}': {'0': '{q0q1}', '1': '{q2}'},
'{q2}': {'0': '{}', '1': '{}'}
})
nose.assert_equal(dfa.initial_state, '{q0}')
nose.assert_equal(dfa.final_states, {'{q2}'})
def create_fa(self, expression, alphabet): automata = DFA() automata.set_name(str(expression)) self.FA_list.append(automata) self.add_tab(expression, ['FA', alphabet])