def test_connection():
T0 = np.array([[0, 1], [1, 0]])
T1 = np.array([[1, 0], [0, 1]])
mdp1 = MDP([T0, T1],
input_fcn=lambda m: m,
output_fcn=lambda n: n,
input_name='u',
output_name='z')
T0 = np.array([[1, 0], [1, 0]])
T1 = np.array([[0, 1], [0, 1]])
mdp2 = MDP([T0, T1],
input_fcn=lambda m: m,
output_fcn=lambda n: n,
input_name='z',
output_name='y')
pmdp = mdp1.product(mdp2, lambda n1: set([n1]))
np.testing.assert_almost_equal(
pmdp.T(0).todense(),
np.array([[0, 0, 0, 1], [0, 0, 0, 1], [1, 0, 0, 0], [1, 0, 0, 0]]))
np.testing.assert_almost_equal(
pmdp.T(1).todense(),
np.array([[1, 0, 0, 0], [1, 0, 0, 0], [0, 0, 0, 1], [0, 0, 0, 1]]))
vals1, _ = pmdp.solve_reach(accept=lambda s: s[0] == 0 and s[1] == 1)
np.testing.assert_almost_equal(vals1[0], [0, 1, 0, 0])
vals2, _ = pmdp.solve_reach(accept=lambda s: s[0] == 0 and s[1] == 0)
np.testing.assert_almost_equal(vals2[0], [1, 1, 1, 1])
def test_ltl_synth():
T1 = np.array([[0.25, 0.25, 0.25, 0.25], [0, 1, 0, 0], [0, 0, 1, 0],
[0, 0, 0, 1]])
T2 = np.array([[0, 0, 0, 1], [0, 1, 0, 0], [0, 0, 1, 0], [0.9, 0, 0, 0.1]])
def connection(n):
# map Y1 -> 2^(2^AP)
if n == 1:
return set((('s1', ), )) # { {s1} }
elif n == 3:
return set((('s2', ), )) # { {s2} }
else:
return set(((), ), ) # { { } }
system = MDP([T1, T2])
formula = '( ( F s1 ) & ( F s2 ) )'
dfsa, init, final, _ = formula_to_mdp(formula)
prod = system.product(dfsa, connection)
V, _ = prod.solve_reach(accept=lambda s: s[1] in final)
np.testing.assert_almost_equal(V[0][:, 0], [0.5, 0, 0, 0.5], decimal=4)
def test_connection():
T0 = np.array([[0.5, 0.5], [0, 1.]])
T1 = np.array([[0.2, 0.8], [1, 0]])
T2 = np.array([[0.2, 0.8], [1, 0]])
mdp1 = MDP([T0, T1, T2])
mdp2 = MDP([T0, T1, T2])
mdp3 = MDP([T0, T1, T2])
prod = mdp1.product(mdp2, connection=lambda n: set([1]))
prod = prod.product(mdp3, connection=lambda n: set([2]))
pT = np.kron(np.kron(T0, T1), T2)
np.testing.assert_almost_equal(prod.T(0).todense(), pT)
def test_mdp_dfsa():
def output(n1):
if n1 == 2:
return 1
else:
return 0
T0 = np.array([[0.5, 0.25, 0.25], [0, 1, 0], [0, 0, 1]])
mdp = MDP([T0], output_fcn=output)
T1 = np.array([[1, 0], [0, 1]])
T2 = np.array([[0, 1], [0, 1]])
fsa = MDP([T1, T2])
connection = lambda n1: set([n1])
prod = mdp.product(fsa, connection)
V, _ = prod.solve_reach(accept=lambda y: y[1] == 1)
np.testing.assert_almost_equal(V[0], [[0.5, 1], [0, 1], [1, 1]], decimal=4)
def test_mdp_dfsa_nondet():
def connection(n1):
if n1 == 2:
return set([1])
elif n1 == 1:
return set([1, 0])
else:
return set([0])
T0 = np.array([[0.5, 0.25, 0.25], [0, 1, 0], [0, 0, 1]])
mdp = MDP([T0])
T1 = np.array([[1, 0], [0, 1]])
T2 = np.array([[0, 1], [0, 1]])
fsa = MDP([T1, T2])
prod = mdp.product(fsa, connection)
V, _ = prod.solve_reach(accept=lambda y: y[1] == 1)
np.testing.assert_almost_equal(V[0], [[0.5, 1], [0, 1], [1, 1]], decimal=4)