def test_canonical_mapping():
ax = USet(3, "a")
a0, a1, a2 = ax.all()
bx = USet(2, "b")
b0, b1 = bx.all()
m1 = hd.Map([(b0, b0), (b1, b0)])
m2 = hd.Map([(b0, b0), (b1, b1)])
m3 = hd.Map([(b0, b1), (b1, b0)])
result = list(hd.Mappings(bx, bx).create_cn_iter())
assert result == [m1, m2, m3]
m1 = hd.Map([(b0, a0), (b1, a0)])
m2 = hd.Map([(b0, a0), (b1, a1)])
result = list(hd.Mappings(bx, ax).create_cn_iter())
assert result == [m1, m2]
m1 = hd.Map([(0, a0), (1, a0)])
m2 = hd.Map([(0, a0), (1, a1)])
result = list(hd.Mappings(hd.Range(2), ax).create_cn_iter())
assert result == [m1, m2]
m1 = hd.Map([(0, b0), (1, b0)])
m2 = hd.Map([(0, b0), (1, b1)])
result = list(hd.Mappings(hd.Range(2), bx).create_cn_iter())
assert result == [m1, m2]
def test_mappings_map_class():
r = hd.Range(2)
m = hd.Mappings(r, r, map_class=tuple)
assert m.strict
result = set(m)
expected = {((0, 0), (1, 0)), ((0, 0), (1, 1)), ((0, 1), (1, 0)),
((0, 1), (1, 1))}
assert result == expected
m = hd.Mappings(r, r, map_class=dict)
assert not m.strict
def test_canonical_map_map():
ax = USet(2, "a")
bx = USet(2, "b")
m1 = hd.Mappings(ax, bx)
m2 = hd.Mappings(ax, ax)
m = hd.Mappings(m1, m2)
bf_check(m)
m = hd.Mappings(m1, m1)
bf_check(m)
m = hd.Mappings(m2, m1)
bf_check(m)
def test_mapping_set():
d1 = hd.Range(3)
d2 = hd.Range(4)
m = hd.Mappings(d1, d2)
a = list(m)
for i in xrange(70):
it = m.create_iter(i)
assert list(it) == a[i:]
def test_mapping_generate():
r1 = hd.Range(2)
p = hd.Mappings(r1, r1)
result = list(p.generate(200))
for r in result:
assert len(r) == 2
assert r.get(0) == 0 or r.get(0) == 1
assert r.get(1) == 0 or r.get(1) == 1
def test_canonical_map_prod():
ax = USet(3, "a")
bx = USet(2, "b")
cx = USet(1, "b")
m1 = hd.Mappings(bx, cx)
m2 = hd.Mappings(ax, ax)
m3 = hd.Mappings(ax, bx)
bf_check(m1 * bx)
bf_check(m1 * cx)
bf_check(bx * m1)
bf_check(cx * m1)
bf_check(m1 * m1)
bf_check(m3 * m3)
bf_check(m3 * m3 * m3)
bf_check(m2 * m3)
def test_cannonical_prod_map():
ax = USet(3, "a")
bx = USet(2, "b")
pb = bx * bx
pab = ax * bx
m = hd.Mappings(bx, pb)
bf_check(m)
m = hd.Mappings(pb, bx)
bf_check(m)
m = hd.Mappings(pb, pb)
bf_check(m)
m = hd.Mappings(pab, bx)
bf_check(m)
def test_mapping_to_values():
a = hd.Range(5)
b = hd.Range(6)
c = hd.Mappings(a, b)
v = c.to_values()
assert isinstance(v, hd.Values)
assert list(c) == list(v)
def test_dist_precompute(cluster4):
states = hd.USet(2, "q")
alphabet = hd.USet(2, "a")
delta = hd.Mappings(states * alphabet, states)
r1 = delta.cnfs().run()
r2 = delta.cnfs().run(cluster4.ctx)
assert len(r1) == len(r2)
def test_map_is_canonical():
ax = USet(2, "a")
a1, a2 = ax.all()
bx = USet(2, "b")
b1, b2 = bx.all()
ms = hd.Mappings(ax, bx)
c = [item for item in ms if hdc.is_canonical(item)]
m1 = hd.Map(((a1, b1), (a2, b1)))
m2 = hd.Map(((a1, b1), (a2, b2)))
assert hdt.compare_sequence([m1, m2], c) == 0
ms = hd.Mappings(ax, ax)
c = [item for item in ms if hdc.is_canonical(item)]
m1 = hd.Map(((a1, a1), (a2, a1)))
m2 = hd.Map(((a1, a1), (a2, a2)))
m3 = hd.Map(((a1, a2), (a2, a1)))
assert hdt.compare_sequence([m1, m2, m3], c) == 0
def test_mapping_to_values_maxsize():
a = hd.Range(5)
b = hd.Range(6)
c = hd.Mappings(a, b)
v = c.to_values(max_size=6)
assert isinstance(v, hd.Mappings)
assert isinstance(v.key_domain, hd.Values)
assert isinstance(v.value_domain, hd.Values)
assert list(c) == list(v)
def test_mapping_int_int():
r = hd.Range(2)
m = hd.Mappings(r, r)
result = list(m)
e1 = hd.Map(((0, 0), (1, 0)))
e2 = hd.Map(((0, 0), (1, 1)))
e3 = hd.Map(((0, 1), (1, 0)))
e4 = hd.Map(((0, 1), (1, 1)))
assert result == [e1, e2, e3, e4]
assert m.size == 4
def test_domain_filter():
def fn(x):
return x > 2 and x < 5
r = hd.Range(6)
d = r.filter(fn)
result = list(d)
assert result == [3, 4]
result = list(d.generate(5))
assert len(result) == 5
for x in result:
assert x in [3, 4]
assert d.filtered
assert not r.filtered
assert d.size == 6
p = d * d
result = list(p)
assert set(result) == {(3, 3), (4, 3), (3, 4), (4, 4)}
assert p.filtered
assert not (r * r).filtered
assert hd.Sequences(d, 2).filtered
assert not hd.Sequences(r, 2).filtered
assert not hd.Mappings(d, r).filtered
assert hd.Mappings(r, d).filtered
assert not hd.Mappings(r, r).filtered
assert hd.Product((d, d), unordered=True).filtered
assert not hd.Product((r, r), unordered=True).filtered
result = list(hd.Product((d, d), unordered=True))
assert set(result) == {(4, 3)}
def main():
n_states = 6 # Number of states
n_symbols = 2 # Number of symbols in alphabet
states = hd.USet(n_states, "q") # set of states q0, q1, ..., q_{n_states}
alphabet = hd.USet(n_symbols, "a") # set of symbols a0, ..., a_{a_symbols}
# Mappings (states * alphabet) -> states
delta = hd.Mappings(states * alphabet, states)
# Let us precompute some values that will be repeatedly used
init_state = frozenset(states)
max_steps = (n_states**3 - n_states) / 6
def check_automaton(delta):
# This function takes automaton as a transition function and
# returns the minimal length of synchronizing word or 0 if there
# is no such word
def step(state, depth):
# A step in bread-first search; gives a set of states
# and return a set reachable by one step
for a in alphabet:
yield frozenset(delta[(s, a)] for s in state)
delta = delta.to_dict()
return search.bfs(
init_state, # Initial state
step, # Step
lambda state, depth: depth if len(state) == 1 else None,
# Run until we reach a single state
max_depth=max_steps, # Limit depth of search
not_found_value=0) # Return 0 when we exceed depth limit
# Create & run pipeline
pipeline = delta.cnfs().map(check_automaton).max(size=1)
result = pipeline.run()
print("The maximal length of a minimal reset word for an "
"automaton with {} states and {} symbols is {}.".format(
n_states, n_symbols, result[0]))
def test_mapping_strict():
r = hd.Range(2)
s = hd.Mappings(r, r)
assert s.strict
def test_mapping_name():
r = hd.Range(10)
m = hd.Mappings(r, r, name="TestMappings")
assert m.name == "TestMappings"
def test_mapping_size():
m = hd.Mappings(hd.Range(10), hd.Range(2))
assert m.size == 1024
def test_mapping_flags():
d1 = hd.Range(3)
d2 = hd.Range(3).filter(lambda x: True)
assert hd.Mappings(d1, d2).filtered
assert not hd.Mappings(d1, d1).filtered