def test_minify_dfa(self):
"""Should minify a given DFA."""
# This DFA accepts all words which are at least two characters long.
# The states q1/q2 and q3/q4/q5/q6 are redundant.
# The state q7 is not reachable.
dfa = DFA(
states={'q0', 'q1', 'q2', 'q3', 'q4', 'q5', 'q6', 'q7'},
input_symbols={'0', '1'},
transitions={
'q0': {'0': 'q1', '1': 'q2'},
'q1': {'0': 'q3', '1': 'q4'},
'q2': {'0': 'q5', '1': 'q6'},
'q3': {'0': 'q3', '1': 'q3'},
'q4': {'0': 'q4', '1': 'q4'},
'q5': {'0': 'q5', '1': 'q5'},
'q6': {'0': 'q6', '1': 'q6'},
'q7': {'0': 'q7', '1': 'q7'},
},
initial_state='q0',
final_states={'q3', 'q4', 'q5', 'q6'}
)
minimal_dfa = dfa.minify()
nose.assert_equal(minimal_dfa.states, {
'q0', '{q1,q2}', '{q3,q4,q5,q6}'
})
nose.assert_equal(minimal_dfa.input_symbols, {'0', '1'})
nose.assert_equal(minimal_dfa.transitions, {
'q0': {'0': '{q1,q2}', '1': '{q1,q2}'},
'{q1,q2}': {'0': '{q3,q4,q5,q6}', '1': '{q3,q4,q5,q6}'},
'{q3,q4,q5,q6}': {'0': '{q3,q4,q5,q6}', '1': '{q3,q4,q5,q6}'}
})
nose.assert_equal(minimal_dfa.initial_state, 'q0')
nose.assert_equal(minimal_dfa.final_states, {'{q3,q4,q5,q6}'})
def test_minify_dfa_initial_state(self):
"""Should minify a DFA where the initial state is being changed."""
# This DFA accepts all words with ones and zeroes.
# The two states can be merged into one.
dfa = DFA(
states={'q0', 'q1'},
input_symbols={'0', '1'},
transitions={
'q0': {
'0': 'q1',
'1': 'q1'
},
'q1': {
'0': 'q0',
'1': 'q0'
},
},
initial_state='q0',
final_states={'q0', 'q1'},
)
minimal_dfa = dfa.minify()
nose.assert_equal(minimal_dfa.states, {'{q0,q1}'})
nose.assert_equal(minimal_dfa.input_symbols, {'0', '1'})
nose.assert_equal(minimal_dfa.transitions, {
'{q0,q1}': {
'0': '{q0,q1}',
'1': '{q0,q1}'
},
})
nose.assert_equal(minimal_dfa.initial_state, '{q0,q1}')
nose.assert_equal(minimal_dfa.final_states, {'{q0,q1}'})
def test_minify_minimal_dfa(self):
"""Should minify an already minimal DFA."""
# This DFA just accepts words ending in 1.
dfa = DFA(
states={'q0', 'q1'},
input_symbols={'0', '1'},
transitions={
'q0': {'0': 'q0', '1': 'q1'},
'q1': {'0': 'q0', '1': 'q1'}
},
initial_state='q0',
final_states={'q1'}
)
minimal_dfa = dfa.minify()
nose.assert_equal(minimal_dfa.states, dfa.states)
nose.assert_equal(minimal_dfa.input_symbols, dfa.input_symbols)
nose.assert_equal(minimal_dfa.transitions, dfa.transitions)
nose.assert_equal(minimal_dfa.initial_state, dfa.initial_state)
nose.assert_equal(minimal_dfa.final_states, dfa.final_states)
def test_minify_dfa_no_final_states(self):
dfa = DFA(
states={'q0', 'q1'},
input_symbols={'0', '1'},
transitions={
'q0': {'0': 'q1', '1': 'q1'},
'q1': {'0': 'q0', '1': 'q0'},
},
initial_state='q0',
final_states=set(),
)
minimal_dfa = dfa.minify()
nose.assert_equal(minimal_dfa.states, {'{q0,q1}'})
nose.assert_equal(minimal_dfa.input_symbols, {'0', '1'})
nose.assert_equal(minimal_dfa.transitions, {
'{q0,q1}': {'0': '{q0,q1}', '1': '{q0,q1}'},
})
nose.assert_equal(minimal_dfa.initial_state, '{q0,q1}')
nose.assert_equal(minimal_dfa.final_states, set())
def test_minify_dfa_complex(self):
dfa = DFA(
states={'13', '56', '18', '10', '15', '26', '24', '54', '32', '27',
'5', '43', '8', '3', '17', '45', '57', '46', '35', '9',
'0', '21', '39', '51', '6', '55', '47', '11', '20', '12',
'59', '38', '44', '52', '16', '41', '1', '4', '28', '58',
'48', '23', '22', '2', '31', '36', '34', '49', '40', '7',
'25', '30', '53', '42', '33', '19', '50', '37', '14',
'29'},
input_symbols={'L', 'U', 'R', 'D'},
transitions={'55': {'L': '20', 'U': '49', 'R': '20', 'D': '49'},
'57': {'L': '5', 'U': '6', 'R': '1', 'D': '46'},
'35': {'L': '44', 'U': '32', 'R': '36', 'D': '33'},
'13': {'L': '45', 'U': '23', 'R': '45', 'D': '23'},
'43': {'L': '44', 'U': '32', 'R': '44', 'D': '33'},
'9': {'L': '5', 'U': '6', 'R': '1', 'D': '6'},
'53': {'L': '20', 'U': '33', 'R': '20', 'D': '32'},
'12': {'L': '40', 'U': '23', 'R': '25', 'D': '11'},
'42': {'L': '1', 'U': '49', 'R': '5', 'D': '49'},
'24': {'L': '40', 'U': '48', 'R': '25', 'D': '23'},
'27': {'L': '5', 'U': '46', 'R': '1', 'D': '6'},
'22': {'L': '40', 'U': '48', 'R': '25', 'D': '11'},
'19': {'L': '36', 'U': '32', 'R': '44', 'D': '33'},
'59': {'L': '40', 'U': '48', 'R': '45', 'D': '11'},
'39': {'L': '45', 'U': '48', 'R': '25', 'D': '11'},
'51': {'L': '20', 'U': '18', 'R': '20', 'D': '18'},
'34': {'L': '5', 'U': '4', 'R': '1', 'D': '31'},
'33': {'L': '44', 'U': '0', 'R': '36', 'D': '28'},
'23': {'L': '45', 'U': '8', 'R': '45', 'D': '8'},
'46': {'L': '44', 'U': '0', 'R': '44', 'D': '28'},
'58': {'L': '5', 'U': '4', 'R': '1', 'D': '4'},
'50': {'L': '20', 'U': '28', 'R': '20', 'D': '0'},
'54': {'L': '40', 'U': '8', 'R': '25', 'D': '41'},
'49': {'L': '1', 'U': '18', 'R': '5', 'D': '18'},
'21': {'L': '40', 'U': '26', 'R': '25', 'D': '8'},
'16': {'L': '5', 'U': '31', 'R': '1', 'D': '4'},
'6': {'L': '40', 'U': '26', 'R': '25', 'D': '41'},
'32': {'L': '36', 'U': '0', 'R': '44', 'D': '28'},
'48': {'L': '40', 'U': '26', 'R': '45', 'D': '41'},
'11': {'L': '45', 'U': '26', 'R': '25', 'D': '41'},
'15': {'L': '14', 'U': '49', 'R': '14', 'D': '49'},
'1': {'L': '56', 'U': '6', 'R': '37', 'D': '46'},
'3': {'L': '4', 'U': '32', 'R': '17', 'D': '33'},
'45': {'L': '8', 'U': '23', 'R': '8', 'D': '23'},
'52': {'L': '4', 'U': '32', 'R': '4', 'D': '33'},
'36': {'L': '56', 'U': '6', 'R': '37', 'D': '6'},
'20': {'L': '14', 'U': '33', 'R': '14', 'D': '32'},
'25': {'L': '47', 'U': '23', 'R': '10', 'D': '11'},
'29': {'L': '37', 'U': '49', 'R': '56', 'D': '49'},
'40': {'L': '47', 'U': '48', 'R': '10', 'D': '23'},
'5': {'L': '56', 'U': '46', 'R': '37', 'D': '6'},
'44': {'L': '47', 'U': '48', 'R': '10', 'D': '11'},
'38': {'L': '17', 'U': '32', 'R': '4', 'D': '33'},
'2': {'L': '47', 'U': '48', 'R': '8', 'D': '11'},
'30': {'L': '8', 'U': '48', 'R': '10', 'D': '11'},
'7': {'L': '14', 'U': '18', 'R': '14', 'D': '18'},
'37': {'L': '56', 'U': '4', 'R': '37', 'D': '31'},
'28': {'L': '4', 'U': '0', 'R': '17', 'D': '28'},
'8': {'L': '8', 'U': '8', 'R': '8', 'D': '8'},
'31': {'L': '4', 'U': '0', 'R': '4', 'D': '28'},
'17': {'L': '56', 'U': '4', 'R': '37', 'D': '4'},
'14': {'L': '14', 'U': '28', 'R': '14', 'D': '0'},
'10': {'L': '47', 'U': '8', 'R': '10', 'D': '41'},
'18': {'L': '37', 'U': '18', 'R': '56', 'D': '18'},
'47': {'L': '47', 'U': '26', 'R': '10', 'D': '8'},
'56': {'L': '56', 'U': '31', 'R': '37', 'D': '4'},
'4': {'L': '47', 'U': '26', 'R': '10', 'D': '41'},
'0': {'L': '17', 'U': '0', 'R': '4', 'D': '28'},
'26': {'L': '47', 'U': '26', 'R': '8', 'D': '41'},
'41': {'L': '8', 'U': '26', 'R': '10', 'D': '41'}},
initial_state='55',
final_states={'15', '24', '54', '32', '27', '5', '43', '57', '3',
'46', '35', '9', '21', '39', '51', '6', '55', '11',
'20', '12', '59', '38', '44', '52', '16', '1', '58',
'48', '22', '2', '36', '34', '49', '40', '25', '30',
'53', '42', '33', '19', '50', '29'})
check_dfa = DFA(
states={'5', '36', '1', '49', '40', '25', '46', '6', '55',
'{0,10,14,17,18,23,26,28,31,37,4,41,45,47,56,8}', '33',
'11', '20', '48', '44', '32'},
input_symbols={'L', 'U', 'R', 'D'},
transitions={
'48':
{'L': '40',
'U': '{0,10,14,17,18,23,26,28,31,37,4,41,45,47,56,8}',
'R': '{0,10,14,17,18,23,26,28,31,37,4,41,45,47,56,8}',
'D': '{0,10,14,17,18,23,26,28,31,37,4,41,45,47,56,8}'},
'44':
{'L': '{0,10,14,17,18,23,26,28,31,37,4,41,45,47,56,8}',
'U': '48',
'R': '{0,10,14,17,18,23,26,28,31,37,4,41,45,47,56,8}',
'D': '11'},
'40':
{'L': '{0,10,14,17,18,23,26,28,31,37,4,41,45,47,56,8}',
'U': '48',
'R': '{0,10,14,17,18,23,26,28,31,37,4,41,45,47,56,8}',
'D': '{0,10,14,17,18,23,26,28,31,37,4,41,45,47,56,8}'},
'33':
{'L': '44',
'U': '{0,10,14,17,18,23,26,28,31,37,4,41,45,47,56,8}',
'R': '36',
'D': '{0,10,14,17,18,23,26,28,31,37,4,41,45,47,56,8}'},
'55': {'L': '20', 'U': '49', 'R': '20', 'D': '49'},
'32':
{'L': '36',
'U': '{0,10,14,17,18,23,26,28,31,37,4,41,45,47,56,8}',
'R': '44',
'D': '{0,10,14,17,18,23,26,28,31,37,4,41,45,47,56,8}'},
'46':
{'L': '44',
'U': '{0,10,14,17,18,23,26,28,31,37,4,41,45,47,56,8}',
'R': '44',
'D': '{0,10,14,17,18,23,26,28,31,37,4,41,45,47,56,8}'},
'25':
{'L': '{0,10,14,17,18,23,26,28,31,37,4,41,45,47,56,8}',
'U': '{0,10,14,17,18,23,26,28,31,37,4,41,45,47,56,8}',
'R': '{0,10,14,17,18,23,26,28,31,37,4,41,45,47,56,8}',
'D': '11'},
'6':
{'L': '40',
'U': '{0,10,14,17,18,23,26,28,31,37,4,41,45,47,56,8}',
'R': '25',
'D': '{0,10,14,17,18,23,26,28,31,37,4,41,45,47,56,8}'},
'11':
{'L': '{0,10,14,17,18,23,26,28,31,37,4,41,45,47,56,8}',
'U': '{0,10,14,17,18,23,26,28,31,37,4,41,45,47,56,8}',
'R': '25',
'D': '{0,10,14,17,18,23,26,28,31,37,4,41,45,47,56,8}'},
'5':
{'L': '{0,10,14,17,18,23,26,28,31,37,4,41,45,47,56,8}',
'U': '46',
'R': '{0,10,14,17,18,23,26,28,31,37,4,41,45,47,56,8}',
'D': '6'},
'49':
{'L': '1',
'U': '{0,10,14,17,18,23,26,28,31,37,4,41,45,47,56,8}',
'R': '5',
'D': '{0,10,14,17,18,23,26,28,31,37,4,41,45,47,56,8}'},
'{0,10,14,17,18,23,26,28,31,37,4,41,45,47,56,8}':
{'L': '{0,10,14,17,18,23,26,28,31,37,4,41,45,47,56,8}',
'U': '{0,10,14,17,18,23,26,28,31,37,4,41,45,47,56,8}',
'R': '{0,10,14,17,18,23,26,28,31,37,4,41,45,47,56,8}',
'D': '{0,10,14,17,18,23,26,28,31,37,4,41,45,47,56,8}'},
'20':
{'L': '{0,10,14,17,18,23,26,28,31,37,4,41,45,47,56,8}',
'U': '33',
'R': '{0,10,14,17,18,23,26,28,31,37,4,41,45,47,56,8}',
'D': '32'},
'36':
{'L': '{0,10,14,17,18,23,26,28,31,37,4,41,45,47,56,8}',
'U': '6',
'R': '{0,10,14,17,18,23,26,28,31,37,4,41,45,47,56,8}',
'D': '6'},
'1':
{'L': '{0,10,14,17,18,23,26,28,31,37,4,41,45,47,56,8}',
'U': '6',
'R': '{0,10,14,17,18,23,26,28,31,37,4,41,45,47,56,8}',
'D': '46'}},
initial_state='55',
final_states={'5', '1', '36', '49', '40', '25', '46', '6', '55',
'33', '11', '20', '48', '44', '32'})
minimal_dfa = dfa.minify()
nose.assert_equal(minimal_dfa.states, check_dfa.states)
nose.assert_equal(minimal_dfa.input_symbols, check_dfa.input_symbols)
nose.assert_equal(minimal_dfa.transitions, check_dfa.transitions)
nose.assert_equal(minimal_dfa.initial_state, check_dfa.initial_state)
nose.assert_equal(minimal_dfa.final_states, check_dfa.final_states)
'0': 'q0',
'1': 'q1'
},
'q1': {
'0': 'q0',
'1': 'q2'
},
'q2': {
'0': 'q2',
'1': 'q1'
}
},
initial_state='q0',
final_states={'q1'})
print('MINIMIZAÇÃO DE AUTOMATO DFA')
minimal_dfa = dfa.minify()
#print(minimal_dfa)
print("Automata symbol", dfa.input_symbols)
print("Automata states", dfa.states)
print("Initiate state", dfa.initial_state)
print("Transitions", dfa.transitions)
print("Final states", dfa.final_states)
print('\n')
# =========================================================================================
# DETERMINIZAÇÃO COM YPSILONE('ε')
print("DETERMINIZATION OF AUTOMATA WITH YPSILONE('ε')")
nfa = NFA(states={'q0', 'q1', 'q2'},
input_symbols={'a', 'b'},
transitions={