def test_derivation_with_general_window():
block = fully_cross_block([color, text, congruent_bookend], [color, text],
[])
# congruent bookend - yes
d = Derivation(16, [[0, 2], [1, 3]], congruent_bookend)
backend_request = BackendRequest(19)
d.apply(block, backend_request)
(expected_cnf, expected_fresh) = to_cnf_tseitin(
And([
Iff(17, Or([And([1, 3]), And([2, 4])])),
Iff(19, Or([And([13, 15]), And([14, 16])]))
]), 19)
assert backend_request.fresh == expected_fresh
assert backend_request.cnfs == [expected_cnf]
# congruent bookend - no
d = Derivation(17, [[0, 3], [1, 2]], congruent_bookend)
backend_request = BackendRequest(19)
d.apply(block, backend_request)
(expected_cnf, expected_fresh) = to_cnf_tseitin(
And([
Iff(18, Or([And([1, 4]), And([2, 3])])),
Iff(20, Or([And([13, 16]), And([14, 15])]))
]), 19)
assert backend_request.fresh == expected_fresh
assert backend_request.cnfs == [expected_cnf]
def test_derivation_with_multiple_transitions():
block = fully_cross_block(
[color, text, color_repeats_factor, text_repeats_factor],
[color, text], [])
# Text repeats derivation
d = Derivation(22, [[2, 6], [3, 7]], text_repeats_factor)
backend_request = BackendRequest(29)
d.apply(block, backend_request)
(expected_cnf, expected_fresh) = to_cnf_tseitin(
And([
Iff(23, Or([And([3, 7]), And([4, 8])])),
Iff(25, Or([And([7, 11]), And([8, 12])])),
Iff(27, Or([And([11, 15]), And([12, 16])]))
]), 29)
assert backend_request.fresh == expected_fresh
assert backend_request.cnfs == [expected_cnf]
# Text does not repeat derivation
d = Derivation(23, [[2, 7], [3, 6]], text_repeats_factor)
backend_request = BackendRequest(29)
d.apply(block, backend_request)
(expected_cnf, expected_fresh) = to_cnf_tseitin(
And([
Iff(24, Or([And([3, 8]), And([4, 7])])),
Iff(26, Or([And([7, 12]), And([8, 11])])),
Iff(28, Or([And([11, 16]), And([12, 15])]))
]), 29)
assert backend_request.fresh == expected_fresh
assert backend_request.cnfs == [expected_cnf]
def test_derivation_with_transition():
block = fully_cross_block([color, text, color_repeats_factor],
[color, text], [])
# Color repeats derivation
d = Derivation(16, [[0, 4], [1, 5]], color_repeats_factor)
backend_request = BackendRequest(23)
d.apply(block, backend_request)
(expected_cnf, expected_fresh) = to_cnf_tseitin(
And([
Iff(17, Or([And([1, 5]), And([2, 6])])),
Iff(19, Or([And([5, 9]), And([6, 10])])),
Iff(21, Or([And([9, 13]), And([10, 14])]))
]), 23)
assert backend_request.fresh == expected_fresh
assert backend_request.cnfs == [expected_cnf]
# Color does not repeat derivation
d = Derivation(17, [[0, 5], [1, 4]], color_repeats_factor)
backend_request = BackendRequest(23)
d.apply(block, backend_request)
(expected_cnf, expected_fresh) = to_cnf_tseitin(
And([
Iff(18, Or([And([1, 6]), And([2, 5])])),
Iff(20, Or([And([5, 10]), And([6, 9])])),
Iff(22, Or([And([9, 14]), And([10, 13])]))
]), 23)
assert backend_request.fresh == expected_fresh
assert backend_request.cnfs == [expected_cnf]
def test_derivation():
# Congruent derivation
d = Derivation(4, [[0, 2], [1, 3]], con_factor)
backend_request = BackendRequest(24)
d.apply(block, backend_request)
(expected_cnf, expected_fresh) = to_cnf_tseitin(
And([
Iff(5, Or([And([1, 3]), And([2, 4])])),
Iff(11, Or([And([7, 9]), And([8, 10])])),
Iff(17, Or([And([13, 15]), And([14, 16])])),
Iff(23, Or([And([19, 21]), And([20, 22])]))
]), 24)
assert backend_request.fresh == expected_fresh
assert backend_request.cnfs == [expected_cnf]
# Incongruent derivation
d = Derivation(5, [[0, 3], [1, 2]], con_factor)
backend_request = BackendRequest(24)
d.apply(block, backend_request)
(expected_cnf, expected_fresh) = to_cnf_tseitin(
And([
Iff(6, Or([And([1, 4]), And([2, 3])])),
Iff(12, Or([And([7, 10]), And([8, 9])])),
Iff(18, Or([And([13, 16]), And([14, 15])])),
Iff(24, Or([And([19, 22]), And([20, 21])]))
]), 24)
assert backend_request.fresh == expected_fresh
assert backend_request.cnfs == [expected_cnf]
def test_derivation_with_unusual_order():
d = Derivation(0, [[4, 2], [5, 3]], congruency)
backend_request = BackendRequest(64)
d.apply(block, backend_request)
(expected_cnf, expected_fresh) = to_cnf_tseitin(
And([
Iff(1, Or([And([5, 3]), And([6, 4])])),
Iff(9, Or([And([13, 11]), And([14, 12])])),
Iff(17, Or([And([21, 19]), And([22, 20])])),
Iff(25, Or([And([29, 27]), And([30, 28])])),
Iff(33, Or([And([37, 35]), And([38, 36])])),
Iff(41, Or([And([45, 43]), And([46, 44])])),
Iff(49, Or([And([53, 51]), And([54, 52])])),
Iff(57, Or([And([61, 59]), And([62, 60])])),
]), 64)
assert backend_request.fresh == expected_fresh
assert backend_request.cnfs == [expected_cnf]
def test_derivation_with_three_level_transition():
f = Factor("f", ["a", "b", "c"])
f_transition = Factor("transition", [
DerivedLevel("aa",
Transition(lambda c: c[0] == "a" and c[1] == "a", [f])),
DerivedLevel("ab",
Transition(lambda c: c[0] == "a" and c[1] == "b", [f])),
DerivedLevel("ac",
Transition(lambda c: c[0] == "a" and c[1] == "c", [f])),
DerivedLevel("ba",
Transition(lambda c: c[0] == "b" and c[1] == "a", [f])),
DerivedLevel("bb",
Transition(lambda c: c[0] == "b" and c[1] == "b", [f])),
DerivedLevel("bc",
Transition(lambda c: c[0] == "b" and c[1] == "c", [f])),
DerivedLevel("ca",
Transition(lambda c: c[0] == "c" and c[1] == "a", [f])),
DerivedLevel("cb",
Transition(lambda c: c[0] == "c" and c[1] == "b", [f])),
DerivedLevel("cc",
Transition(lambda c: c[0] == "c" and c[1] == "c", [f])),
])
block = fully_cross_block([f, f_transition], [f], [])
# a-a derivation
d = Derivation(9, [[0, 3]], f_transition)
backend_request = BackendRequest(28)
d.apply(block, backend_request)
(expected_cnf, expected_fresh) = to_cnf_tseitin(
And([Iff(10, Or([And([1, 4])])),
Iff(19, Or([And([4, 7])]))]), 28)
assert backend_request.fresh == expected_fresh
assert backend_request.cnfs == [expected_cnf]