def absorbtion(A, B):
global count
assert identity(union([A, intersection([A.clone(), B.clone()])]), A.clone())
assert identity(intersection([A, union([A.clone(), B.clone()])]), A.clone())
count += 1
def domination(A):
global count
first = union([A, DFA.Universal()])
assert identity(first, DFA.Universal())
first = intersection([A, DFA.Empty()])
assert identity(first, DFA.Empty())
count += 1
def complement_laws(A):
global count
first = union([A.clone(), complement(A.clone())])
assert identity(first, DFA.Universal())
first = intersection([A.clone(), complement(A.clone())])
assert identity(first, DFA.Empty())
count += 1
def identity_vs_empty_and_universal(A):
global count
count += 1
# if count != 3: return
first = union([A.clone(), DFA.Empty()])
assert identity(first, A.clone())
first = intersection([A.clone(), DFA.Universal()])
assert identity(first, A)
def de_morgan(A, B):
global count
assert identity(
complement(union([A.clone(), B.clone()])),
intersection([complement(A.clone()),
complement(B.clone())]))
assert identity(complement(intersection([A.clone(), B.clone()])),
union([complement(A.clone()),
complement(B.clone())]))
count += 1
def distributivity(A, B, C):
global count
first = union([A.clone(), intersection([B.clone(), C.clone()])])
second = intersection([union([A.clone(), B.clone()]), union([A.clone(),C.clone()])])
assert identity(first, second)
first = intersection([A.clone(), union([B.clone(), C.clone()])])
second = union([intersection([A.clone(), B.clone()]), intersection([A.clone(),C.clone()])])
assert identity(first, second)
count += 1
def commutativity(A, B):
global count
first = union([A.clone(), B.clone()])
second = union([B.clone(), A.clone()])
assert identity(first, second)
first = intersection([A.clone(), B.clone()])
second = intersection([B.clone(), A.clone()])
assert identity(first, second)
count += 1
def uniqueness(A):
"""Uniqueness of complement:
A u B = Universal and A n B = Empty
=> A = complement B and vice versa
Involution:
A = complement(complement(A))
"""
global count
B = difference(DFA.Universal(), A)
# => A u B = Universal and A n B = Empty
assert identity(union([A, B]), DFA.Universal())
assert identity(intersection([A, B]), DFA.Empty())
# Uniqueness of complement
assert identity(A, complement(B))
assert identity(B, complement(A))
# Involution/Double Complement
assert identity(A, complement(complement(A)))
assert identity(B, complement(complement(B)))
count += 1
def intersection_by_difference(A, B):
global count
assert identity(intersection([A, B]), difference(A, difference(A, B)))
count += 1