def mkp_dfa(Q, Sigma, Delta, q0, F):
"""In : Traits of a DFA
Out: A DFA
Check for partial consistency of the given DFA traits.
If the check passes, make and return a DFA with a partial
Delta.
"""
newDFA = {"Q": Q, "Sigma": Sigma, "Delta": Delta, "q0": q0, "F": F}
assert (
is_partially_consistent_dfa(newDFA)
), "DFA given to mkp_dfa is not partially consistent. Plz check its components."
return (newDFA)
def totalize_dfa(D):
"""In : Partially consistent DFA
Out: A consistent DFA
Given a partially specified DFA, make it total by
transitioning to state BH wherever the incoming Delta
has gaps. The returned DFA is structurally consistent.
"""
assert (is_partially_consistent_dfa(D)
), "DFA given to totalize_dfa is not partially consistent."
if set(fn_dom(D["Delta"])) == set(product(D["Q"], D["Sigma"])):
# It is already total!
return D
else:
# We must introduce a BH state of not already present
# and proceed from there
incoming_Delta = D["Delta"].copy()
# Gaps in incoming_Delta's transition function are sent
# to the BH (black-hole) state
gaps_in_Tr = {(q, c): "BH"
for q in D["Q"] for c in D["Sigma"]
if (q, c) not in D["Delta"]}
# We are gonna add a new black-hole-state.
# It must curl back to itself for every symbol in Sigma
bh_self_absorbent_moves = {("BH", c): "BH" for c in D["Sigma"]}
# Fill the gaps in incoming_Delta
incoming_Delta.update(gaps_in_Tr)
# Add in the moves where the black-hole state curls
# back to itself
incoming_Delta.update(bh_self_absorbent_moves)
# All updates required are accomplished
finished_Delta = incoming_Delta
# See that we update D["Q"] with the "BH" (black-hole)
# state; also return the fixed-up incoming_Delta
return {
"Q": D["Q"] | {"BH"},
"Sigma": D["Sigma"],
"Delta": finished_Delta,
"q0": D["q0"],
"F": D["F"]
}