def test__linearize_regular_expression(self):
re1 = parse_regular_expression('a (a + b + ε)* a')
lin1, idx1 = _linearize_regular_expression(re1)
self.assertEqual(idx1, 4)
self.assertEqual(len(lin1.alphabet()), 4)
self.assertEqual(
repr(lin1).replace(' ', ''),
'CONCAT(CONCAT(a0, STAR(PLUS(PLUS(a1, b2), ε))), a3)'
.replace(' ', '')
)
re2 = parse_regular_expression('a a a a a a a')
lin2, idx2 = _linearize_regular_expression(re2)
self.assertEqual(idx2, 7)
self.assertEqual(len(lin2.alphabet()), 7)
def residual_automaton(
regular_expression: RegularExpression) -> FiniteAutomaton:
"""From a regular expression, constructs an equivalent finite automaton
using the residuals method
"""
initial_state = _state_identifier(regular_expression)
accepting_states = []
alphabet = regular_expression.alphabet()
transitions: Dict[State, List[Tuple[Letter, State]]] = {}
unexplored_states = [initial_state]
while unexplored_states:
state = unexplored_states.pop(0)
state_re = parse_regular_expression(state)
if state_re.accepts_epsilon():
accepting_states.append(state)
transitions[state] = []
for letter in alphabet:
next_residual = residual(state_re, letter)
next_state = _state_identifier(next_residual)
if next_residual is not None:
transitions[state].append((letter, next_state))
# Equivalent re can have different string representations...
if next_state not in transitions:
transitions[next_state] = []
unexplored_states.append(next_state)
return FiniteAutomaton(alphabet=alphabet,
states=set(transitions.keys()),
initial_states={initial_state},
accepting_states=set(accepting_states),
transitions=transitions)
def test_thompson_letter(self):
alphabet = {'a', 'b'}
automaton = thompson(parse_regular_expression('a'), alphabet)
automaton.draw(name='ThompsonTest.test_thompson_letter').render(
directory='out/', format='pdf')
self.assertTrue(automaton.read('a'))
self.assertFalse(automaton.read('b'))
self.assertFalse(automaton.read(''))
def test_glushkov(self):
aut1 = glushkov(parse_regular_expression('a b'))
aut1.draw(
name='GlushkovTest.test_glushkov.1'
).render(directory='out/', format='pdf')
self.assertTrue(aut1.read("ab"))
self.assertFalse(aut1.read(""))
self.assertFalse(aut1.read("a"))
self.assertFalse(aut1.read("b"))
self.assertFalse(aut1.read("ba"))
self.assertFalse(aut1.read("aba"))
aut2 = glushkov(parse_regular_expression('(a b)* (c + ε) d'))
aut2.draw(
name='GlushkovTest.test_glushkov.2'
).render(directory='out/', format='pdf')
self.assertTrue(aut2.read("d"))
self.assertTrue(aut2.read("abababd"))
self.assertTrue(aut2.read("ababcd"))
self.assertFalse(aut2.read(""))
self.assertFalse(aut2.read("ab"))
self.assertFalse(aut2.read("abccd"))
self.assertFalse(aut2.read("ccd"))
aut3 = glushkov(parse_regular_expression('(a (ab)*)*'))
aut3.draw(
name='GlushkovTest.test_glushkov.3'
).render(directory='out/', format='pdf')
self.assertTrue(aut3.read(""))
self.assertTrue(aut3.read("aaaaaa"))
self.assertTrue(aut3.read("aababaaaabab"))
self.assertFalse(aut3.read("b"))
self.assertFalse(aut3.read("bab"))
aut4 = glushkov(parse_regular_expression('(a (b + bbabb)* c)*'))
aut4.draw(
name='GlushkovTest.test_glushkov.4'
).render(directory='out/', format='pdf')
self.assertTrue(aut4.read(""))
self.assertTrue(aut4.read("ac"))
self.assertTrue(aut4.read("acac"))
self.assertTrue(aut4.read("abbcabbabbc"))
self.assertFalse(aut4.read("aac"))
self.assertFalse(aut4.read("abbabc"))
def test_accepts_epsilon(self):
self.assertTrue(parse_regular_expression('ε').accepts_epsilon())
self.assertTrue(parse_regular_expression('a*').accepts_epsilon())
self.assertTrue(parse_regular_expression('a + ε').accepts_epsilon())
self.assertTrue(parse_regular_expression('(a + b)*').accepts_epsilon())
self.assertFalse(parse_regular_expression('a').accepts_epsilon())
self.assertFalse(parse_regular_expression('a* b').accepts_epsilon())
def test_successors(self):
re1 = parse_regular_expression('a b')
self.assertEqual(re1.successors('a'), {'b'})
self.assertEqual(re1.successors('b'), set())
self.assertEqual(re1.successors('c'), set())
re2 = parse_regular_expression('(a + b)*')
self.assertEqual(re2.successors('a'), {'a', 'b'})
self.assertEqual(re2.successors('b'), {'a', 'b'})
self.assertEqual(re2.successors('c'), set())
re3 = parse_regular_expression('a b a c')
self.assertEqual(re3.successors('a'), {'b', 'c'})
self.assertEqual(re3.successors('b'), {'a'})
self.assertEqual(re3.successors('c'), set())
re4 = parse_regular_expression('(a b)* (c + ε) d')
self.assertEqual(re4.successors('a'), {'b'})
self.assertEqual(re4.successors('b'), {'a', 'c', 'd'})
self.assertEqual(re4.successors('c'), {'d'})
self.assertEqual(re4.successors('d'), set())
re5 = parse_regular_expression('(a+ε)(b+ε)(c+ε)(d+ε)')
self.assertEqual(re5.successors('a'), {'b', 'c', 'd'})
self.assertEqual(re5.successors('b'), {'c', 'd'})
self.assertEqual(re5.successors('c'), {'d'})
self.assertEqual(re5.successors('d'), set())
re6 = parse_regular_expression('(a (bc)*)*')
self.assertEqual(re6.successors('a'), {'a', 'b'})
self.assertEqual(re6.successors('b'), {'c'})
self.assertEqual(re6.successors('c'), {'a', 'b'})
def test_alphabet(self):
self.assertEqual(parse_regular_expression('ε').alphabet(), set())
self.assertEqual(parse_regular_expression('a*').alphabet(), {'a'})
self.assertEqual(parse_regular_expression('a + ε').alphabet(), {'a'})
self.assertEqual(
parse_regular_expression('(a + b)*').alphabet(), {'a', 'b'})
self.assertEqual(parse_regular_expression('a').alphabet(), {'a'})
self.assertEqual(
parse_regular_expression('a* b').alphabet(), {'a', 'b'})
def test_brozozwski_minimize(self):
alphabet = {'a', 'b', 'c', 'd'}
automaton1 = brozozwski_minimize(
thompson(parse_regular_expression('abcd'), alphabet)
)
automaton1.draw(
name='BrozozwskiMinimizeTest.test_brozozwski_minimize.automaton1'
).render(directory='out/', format='pdf')
self.assertEqual(len(automaton1.states), 5)
self.assertTrue(automaton1.read('abcd'))
self.assertFalse(automaton1.read('a'))
self.assertFalse(automaton1.read('ab'))
self.assertFalse(automaton1.read('abc'))
self.assertFalse(automaton1.read('bcda'))
self.assertFalse(automaton1.read('dcbaa'))
def test_initial_letters(self):
self.assertEqual(
parse_regular_expression("ε").initial_letters(), set())
self.assertEqual(
parse_regular_expression("a").initial_letters(), {'a'})
self.assertEqual(
parse_regular_expression("a b").initial_letters(), {'a'})
self.assertEqual(
parse_regular_expression("a + b").initial_letters(), {'a', 'b'})
self.assertEqual(
parse_regular_expression("a* b").initial_letters(), {'a', 'b'})
self.assertEqual(
parse_regular_expression("a b*").initial_letters(), {'a'})
self.assertEqual(
parse_regular_expression("(a + b)* (c + ε)").initial_letters(),
{'a', 'b', 'c'})
self.assertEqual(
parse_regular_expression("(c + ε) (a + b)*").initial_letters(),
{'a', 'b', 'c'})
def test_parse(self):
problems = [("ε", "ε"), ("a", "a"), ("a b", "CONCAT(a, b)"),
("ab", "CONCAT(a, b)"), ("ε b", "b"), ("b ε", "b"),
("ε b ε", "b"), ("ε ε ε", "ε"), ("b ε ε", "b"),
("a*", "STAR(a)"), ("a**", "STAR(a)"),
("a + b", "PLUS(a, b)"), ("(a + b)", "PLUS(a, b)"),
("a + ab", "PLUS(a, CONCAT(a, b))"),
("ba + ab", "PLUS(CONCAT(b, a), CONCAT(a, b))"),
("a (a + ε) b", "CONCAT(CONCAT(a, PLUS(a, ε)), b)"),
("(a + b)*", "STAR(PLUS(a, b))"),
("(a + b*)aa b",
"CONCAT(CONCAT(CONCAT(PLUS(a, STAR(b)), a), a), b)"),
("a (a + b*)*", "CONCAT(a, STAR(PLUS(a, STAR(b))))"),
("((a))", "a")]
for problem, solution in problems:
self.assertEqual(
repr(parse_regular_expression(problem)).replace(" ", ""),
solution.replace(" ", ""),
f'Failed regular expression: {problem}')
def brozozwski(automaton: FiniteAutomaton) -> RegularExpression:
"""Implementation of Brozozwski's algorithm for regular expressions
"""
q_init = 'init'
q_acc = 'acc'
table: Dict[State, Dict[State, str]] = {q_acc: {}, q_init: {}}
for state in automaton.initial_states:
table[q_init][state] = 'ε'
for state in automaton.states:
table[state] = {}
for letter, next_state in automaton.transitions.get(state, []):
if next_state in table[state]:
table[state][next_state] += '+' + letter
else:
table[state][next_state] = letter
for state in automaton.accepting_states:
table[state][q_acc] = 'ε'
states_to_remove = list(automaton.states)
states_to_remove.sort()
while states_to_remove:
q_i = states_to_remove.pop()
for q_k in states_to_remove + [q_init, q_acc]:
if q_k == q_i:
continue
for q_l in states_to_remove + [q_init, q_acc]:
if q_l == q_i:
continue
e_kl = table[q_k].get(q_l, '')
e_ki = table[q_k].get(q_i, '')
e_ii = table[q_i].get(q_i, '')
e_il = table[q_i].get(q_l, '')
table[q_k][q_l] = _plus(
e_kl, _concat(_concat(e_ki, _star(e_ii)), e_il))
return parse_regular_expression(table[q_init].get(q_acc, ''))
def test_residual_automaton(self):
automaton1 = residual_automaton(parse_regular_expression('a'))
automaton1.draw(
name='ResidualTest.test_residual_automaton.automaton1').render(
directory='out/', format='pdf')
self.assertTrue(automaton1.read('a'))
self.assertFalse(automaton1.read(''))
self.assertFalse(automaton1.read('aa'))
self.assertFalse(automaton1.read('b'))
self.assertFalse(automaton1.read('ab'))
automaton2 = residual_automaton(parse_regular_expression('ab'))
automaton2.draw(
name='ResidualTest.test_residual_automaton.automaton2').render(
directory='out/', format='pdf')
self.assertTrue(automaton2.read('ab'))
self.assertFalse(automaton2.read(''))
self.assertFalse(automaton2.read('a'))
self.assertFalse(automaton2.read('aa'))
self.assertFalse(automaton2.read('b'))
self.assertFalse(automaton2.read('aba'))
automaton3 = residual_automaton(parse_regular_expression('a*'))
automaton3.draw(
name='ResidualTest.test_residual_automaton.automaton3').render(
directory='out/', format='pdf')
self.assertTrue(automaton3.read(''))
self.assertTrue(automaton3.read('a'))
self.assertTrue(automaton3.read('aa'))
self.assertTrue(automaton3.read('aaa'))
self.assertFalse(automaton3.read('b'))
self.assertFalse(automaton3.read('aaaab'))
automaton4 = residual_automaton(parse_regular_expression('a + b'))
automaton4.draw(
name='ResidualTest.test_residual_automaton.automaton4').render(
directory='out/', format='pdf')
self.assertTrue(automaton4.read('a'))
self.assertTrue(automaton4.read('b'))
self.assertFalse(automaton4.read(''))
self.assertFalse(automaton4.read('ab'))
self.assertFalse(automaton4.read('ba'))
automaton5 = residual_automaton(
parse_regular_expression('(ab + c)* d'))
automaton5.draw(
name='ResidualTest.test_residual_automaton.automaton5').render(
directory='out/', format='pdf')
self.assertTrue(automaton5.read('d'))
self.assertTrue(automaton5.read('abd'))
self.assertTrue(automaton5.read('cd'))
self.assertTrue(automaton5.read('abcd'))
self.assertTrue(automaton5.read('ababd'))
self.assertFalse(automaton5.read(''))
self.assertFalse(automaton5.read('ab'))
self.assertFalse(automaton5.read('ad'))
self.assertFalse(automaton5.read('abad'))
automaton6 = residual_automaton(parse_regular_expression('(a b b*)*'))
automaton6.draw(
name='ResidualTest.test_residual_automaton.automaton6').render(
directory='out/', format='pdf')
self.assertTrue(automaton6.read(''))
self.assertTrue(automaton6.read('ab'))
self.assertTrue(automaton6.read('abb'))
self.assertTrue(automaton6.read('abab'))
self.assertTrue(automaton6.read('abbab'))
self.assertFalse(automaton6.read('a'))
self.assertFalse(automaton6.read('b'))
self.assertFalse(automaton6.read('c'))
self.assertFalse(automaton6.read('abababababaabababab'))
def test_residual(self):
self.assertIsNone(residual(None, ''))
self.assertIsNone(residual(None, 'a'))
self.assertEqual(str(residual(parse_regular_expression('a'), 'a')),
'ε')
self.assertIsNone(residual(parse_regular_expression('a'), 'b'))
self.assertEqual(str(residual(parse_regular_expression('a b'), 'a')),
'b')
self.assertIsNone(residual(parse_regular_expression('a b'), 'b'))
self.assertEqual(str(residual(parse_regular_expression('a + b'), 'a')),
'ε')
self.assertEqual(str(residual(parse_regular_expression('a + b'), 'b')),
'ε')
self.assertEqual(
str(residual(parse_regular_expression('(a + b) c'), 'a')), 'c')
self.assertEqual(
str(residual(parse_regular_expression('(a + b) c'), 'b')), 'c')
self.assertIsNone(residual(parse_regular_expression('(a + b) c'), 'c'))
self.assertEqual(
str(residual(parse_regular_expression('(aa + bb) cc'),
'a')).replace(' ', ''), 'acc')
self.assertEqual(
str(residual(parse_regular_expression('(aa + bb) cc'),
'b')).replace(' ', ''), 'bcc')
self.assertIsNone(
residual(parse_regular_expression('(aa + bb) cc'), 'c'))
self.assertEqual(
str(residual(parse_regular_expression('(aa + ab) cc'),
'a')).replace(' ', ''), '(a+b)cc')
self.assertEqual(
str(residual(parse_regular_expression('(a + b)* a'),
'a')).replace(' ', ''),
'(a + b)* a + ε'.replace(' ', ''))
self.assertEqual(
str(residual(parse_regular_expression('(a + b)* a'),
'b')).replace(' ', ''), '(a + b)* a'.replace(' ', ''))
self.assertIsNone(residual(parse_regular_expression('(a + b)* a'),
'c'))
self.assertEqual(
str(residual(parse_regular_expression('(abc)* a'),
'a')).replace(' ', ''),
'b c (abc)* a + ε'.replace(' ', ''))
self.assertEqual(
str(residual(parse_regular_expression('(abc)* a'),
'ab')).replace(' ', ''),
'c (abc)* a'.replace(' ', ''))
self.assertEqual(
str(residual(parse_regular_expression('(a+ε)(b+ε)(c+ε)(d+ε)'),
'a')).replace(' ', ''),
'(b + ε)(c + ε)(d + ε)'.replace(' ', ''))
self.assertEqual(
str(residual(parse_regular_expression('(a+ε)(b+ε)(c+ε)(d+ε)'),
'b')).replace(' ', ''),
'(c + ε)(d + ε)'.replace(' ', ''))
self.assertEqual(
str(residual(parse_regular_expression('(a+ε)(b+ε)(c+ε)(d+ε)'),
'c')).replace(' ', ''), 'd + ε'.replace(' ', ''))
self.assertEqual(
str(
residual(parse_regular_expression('(a+ε)(b+ε)(c+ε)(d+ε)'),
'ab')).replace(' ', ''),
'(c + ε) (d + ε)'.replace(' ', ''))
def test___eq__(self):
self.assertEqual(parse_regular_expression('a'),
parse_regular_expression('a'))
self.assertNotEqual(parse_regular_expression('a'),
parse_regular_expression('b'))
self.assertEqual(parse_regular_expression('ε'),
parse_regular_expression('ε'))
self.assertNotEqual(parse_regular_expression('ε'),
parse_regular_expression('b'))
self.assertEqual(parse_regular_expression('a + b'),
parse_regular_expression('a + b'))
self.assertNotEqual(parse_regular_expression('a'),
parse_regular_expression('a + b'))
self.assertNotEqual(parse_regular_expression('b + a'),
parse_regular_expression('a + b'))
self.assertEqual(parse_regular_expression('(a + b)* c'),
parse_regular_expression('(a + b)* c'))
self.assertNotEqual(parse_regular_expression('(a + b)* c'),
parse_regular_expression('a* c'))
self.assertNotEqual(parse_regular_expression('(a + b)* c'),
parse_regular_expression('(a + b) c'))
