def synchro_prod_poly_example():
A = NFA.spec("""
0
1
0 a 1 c 1
1 a 0""").named("A").visu()
B = NFA.spec("""
0
1
0 b 1 c 1
1 b 0""").renum(2).named("B").visu()
_ = NFA.Stay
C = NFA.sprod(A, B, svec={("a", _), (_, "b"),
("c", "c")}).visu() # .texvisu(renum=True)
D = A | B | C
D.visu().texvisu(renum=True,
at={
'0': (0, .5),
'1': (1, .5),
'2': (-.5, 0),
'3': (-.5, -1),
'(0, 2)': (0, 0),
'(1, 2)': (1, 0),
'(0, 3)': (0, -1),
'(1, 3)': (1, -1),
}.get,
params=",x=3cm,y=3cm")
def revision_interro():
NFA.spec("""
1
2
1 a 1 a 2 b 2 eps 3
2 b 2
3 a 3
""",
name="Révision ε-removal").visu().rm_eps().visu().dfa().visu(
).mini().visu()
NFA({1}, {3}, {(1, "a", 2), (2, "b", 3), (3, "c", 2), (3, '', 1)},
name="ε2").visu().rm_eps().visu().dfa().visu().mini().visu()
def minimisation_exo():
NFA.spec(
"""
a
c f g
a 0 b 1 e
b 0 b 1 c
e 0 e 1 f
f 1 c 0 b
c 1 f 0 e
d 0 c 1 g
g 0 d 1 f
""",
name="Minimisation exo",
Qtype=str).visu().trim().visu().dfa().visu().mini(table=False).visu()
def rm_esp_clos_test():
A = NFA.spec("""
0
2
0 eps 1
1 eps 2
2 a 0
""").visu().rm_eps().visu()
def verif_mini_prog():
prog = NFA.spec("""
1
__
1 b=1 1 b=0 2
2 b:=1 3
3 proc() 4
4 b:=0 1""").visu().texvisu("1 > 2 > 3 > 4", "4 < 1")
def interro201819():
A = NFA.spec("""
0
5
0 a 1 c 2
1 b 1 a 3
2 b 2 a 4
3 c 3 a 5 a 2
4 c 3 a 5 a 1
""",
name="interro2018-2019").visu()
# A.table()
A.texvisu("0 / 1 > 3\n 0 \ 2 > 4 / 5", "3 ns,c 2 4 ne,c 1 2 lb 2")
A = A.dfa().visu().texvisu(renum=True)
A.mini().visu().texvisu(renum=True)
B = NFA.spec("""
eps
fi
eps a a c c
a b ab a aa
c b cb a ca
ab a aba b ab
cb a cba b cb
aba c ac
aa c ac a fi
ca a fi c ac
cba a fi c ac
ac c ac a fi
""",
name="StudentMini").visu().mini().visu()
C = NFA.spec("""
I
IV
I a II c II
II b II a III
III c III a IV
""",
name="RealMini").visu()
(C - B).visu().mini().visu()
(C | B).visu()
def exam2020():
A = NFA.spec("""
1 2
1
1 a 1 b 2
2 a 3 b 2
3 a 3 b 1""").visu()
A.texvisu()
A.texvisu("1 _ 2 > 3", "1 la 1 2 lb 2 3 la 3 3 ~ 1")
A.dfa().visu().mini().visu()
def simplifyArdenSystem():
ard = NFA.spec("""
A
C A
A 0 B 1 C
B 0 C
C 0 C 1 C eps A
""",
name="Arden").visu().mini().visu()
(-ard).mini().visu()
def exoEqualRegexp():
A = NFA.spec("""
1 3
4
1 a 2 a 3
2 b 3
3 a 4 eps 1""").named("A").visu()
B = NFA.spec("""
1
4 2
1 a 2
2 b 3 a 4
3 a 4
4 eps 2""").named("B").visu()
A = A.rm_eps().visu()
B = B.rm_eps().visu()
A = A.dfa().visu()
B = B.dfa().visu().complete().visu().mini().visu()
def testproducts():
NFA.VISULANG = 5
NFA.VISU_INITIAL_ARROW = False
Char = NFA.spec("""
0
1
0 1 1
1 0 0
""").map(g=int).named("Char").visu()
_ = NFA.Stay
C1 = Char.copy().map(g=lambda x: "b" if x else "a").named("C1")
C2 = Char.copy().map(g=lambda x: "B" if x else "A").named("C2")
from itertools import product
NFA._sprod2_brutal(Char, Char, {(0, 0), (1, 1)}).visu()
NFA._sprod2_brutal(Char, Char, set(product([0, 1], repeat=2))).visu()
NFA._sprod2_brutal(Char, Char, {(_, 0), (_, 1), (1, _)}).visu()
NFA._sprod2_brutal(Char, Char, {(_, 0), (_, 1), (1, 1)}).visu()
NFA._sprod2_brutal(Char, Char,
{x
for y in [0, 1] for x in {(_, y), (y, _)}}).visu()
(Char @ Char).visu()
C1.visu()
NFA._sprod2_brutal(Char, C1, set(product([0, 1, _], ["a", 'b', _]))).visu()
(NFA.of_word([1, 2, 3]) @ NFA.of_word([_, _])).visu()
NFA.sprod_brutal(Char, C1, svec=set(product([0, 1, _],
["a", 'b', _]))).visu()
X = NFA.sprod_brutal(Char,
C1,
C2,
svec=set(
product([0, 1, _], ["a", 'b', _],
["A", "B", _]))).visu()
Y = NFA.sprod_brutal(Char,
Char,
Char,
svec=set(product([0, 1, _], repeat=3))).visu()
# on the fly version tests
svec = NFA.shuffle([1, 1], [_]) | NFA.shuffle([0], [_, _])
P = NFA.sprod_brutal(Char, Char, Char, svec=svec).visu()
svec = NFA.shuffle([1, 1], [_]) | NFA.shuffle([0], [_, _])
P = NFA.sprod(Char, Char, Char, svec=svec, record_steps=True).visu()
P.visusteps(P._grow_step)
svec = {(1, 1)}
P = NFA.sprod_brutal(Char, Char, svec=svec, silent=[0]).visu()
Q = NFA.sprod(Char, Char, svec=svec, silent=[0]).visu()
NFA.VISULANG = 10
NFA.VISU_INITIAL_ARROW = True
def isomorphisms():
IH = NFA.spec("""
0
0
0 B 0 A 1
1 A 0
""",
name="(AA|B)*")
IH.visu().complete().visu().ihomo({'a': 'AB', 'b': 'BA'}).visu()
IH.ihomo_visu({'a': 'AB', 'b': 'BA'})
IH.complete().ihomo_visu({'a': 'AB', 'b': 'BA'})
def even_odd():
P = NFA.spec(
"""
P I
P I Ia Paa
P a Pa b P
Pa a Paa
Paa a Pa b I
I b I a Ia
Ia a Iaa b P
Iaa a Ia
""",
name="a_blocks_alternate_even_odd").visu().dfa().visu().mini().visu()
def hard_minimisation():
tab = False
def fib(n):
if n == 0: return "0"
if n == 1: return "1"
return fib(n - 1) + fib(n - 2)
def FIB(n):
return {fib(k) for k in range(n)}
S = FIB(6)
A = NFA.of_set(S).dfa().renum().visu().mini(table=tab).visu()
# starts with final, need to ensure I, II and not II, I, prev bug.
B = NFA.spec("""
0
0
0 a 1 b 1
1 b 0 a 1
""").visu().mini(table=tab).visu()
C = NFA.of_word("aaaa").complete().visu().mini(table=tab).visu()
#!/usr/bin/env python3
from nfa import NFA
NFA.clear() # clean visu.pdf on each run
# NFA.NOVISU=True # check that all runs without generating PDFs
A = NFA.spec("""
0
2
0 a 1 a 2
1 a 0 b 2
""",name="A").visu()
A.run("aaab")
B = NFA.spec("""
0
0
0 c 1 a 0
1 c 0""", name="B").visu()
NFA.visutext("DETERMINISATION")
A.visu().dfa().visu(doublearrows=True)
NFA.visutext("PRODUCTS")
from itertools import product
A.visu(); B.visu()
(A & B).visu().dfa().visu().mini().visu()
def interfaceAutomataProduct():
NFA.VISULANG = 0
client = NFA.spec("""
1
1
1 msg! 2
2 ok? 1""").named("client").visu()
comp = NFA.spec("""
1
1
1 msg? 2
2 envoyer! 3
3 nack? 4 ack? 6
4 envoyer! 5
5 ack? 6 nack? 7
6 ok! 1
7 echec! 1
""").named("comp").visu()
comp_client = NFA.interface_sprod(comp, client, visu_dnice=True).visu()
canal = NFA.spec("""
1
1
1 envoyer? 2
2 token! 3
3 ack! 4
4 liberer_token! 1
D nack! D
""").named("canal").visu()
# print(canal)
canal_comp_client = NFA.interface_sprod(
comp_client, canal, visu_dnice=True).visu().trim().visu()
NFA.VISULANG = 10
Vendor = NFA.spec("""
0
7
0 pay? 1
## 1 deliver! 2
1 verif! 3
## 2 verif! 4
3 deliver! 4 transfer? 5
4 transfer? 7
5 deliver! 7
""",
name="Vendor",
worder=tuple)
Vendor.visu()
Client = NFA.spec("""
0
0
0 pay! 0 deliver? 0 cancel! 0
""",
name="Client",
worder=tuple)
Client.visu()
Bank = NFA.spec("""
0
1 3
0 cancel? 1
0 verif? 2
2 transfer! 3
""",
name="Bank",
worder=tuple)
Bank.visu()
CB = NFA.interface_sprod(Client, Bank).visu()
Sys = NFA.interface_sprod(CB, Vendor).visu()
def ctl_tests():
from ctl import AND, OR, NOT, TT, FF, IMPLIES, XOR, EX, EU, AU, AX, AG, EG, AF, EF, checkvisu
n = NFA.VISULANG
NFA.VISULANG = 0
p, q = "pq"
exo = NFA.spec("""
0
__
0 1 2
1 0
2 3 5 9
3 2 4 6
4 5
5 1 6 7
6 9
7 1 2
8 8
9 1 6 9
10 8
11 10 2
""",
name="Exo1-exam17",
style="ts")
labels = {
1: {p},
4: {p},
6: {p},
7: {p},
8: {q, p},
9: {p, q},
10: {p},
11: {p}
}
# exo.label(labels,f_str).visu()
# fo = (OR, (AND, (EX, p), (NOT,p)), p)
# fo = (OR, p, (NOT, p))
# fo = (OR, (NOT, (EX, (NOT, p))), (AX, p))
# fo = (IMPLIES, p, q)
# fo = (IMPLIES, (NOT, p), (AX, p))
# fo = (XOR, p, (AX, p))
# fo = (AND, (AU, TT, q), (AF,q))
# fo = (EF, q)
# fo = (AND, (NOT, (EU, TT, (NOT, p))), (AG, p))
# fo = (AG, p)
fo = (AND, (EG, q), (EG, p), (EG, (OR, p, q)), (AG, (OR, p, q)))
checkvisu(exo, labels, fo)
kat = NFA.spec("""
0
__
0 1 2
1 0 3
2 1
3 3
""",
name="Katoen examples",
style="ts").visu()
labels = {0: {p}, 1: {p, q}, 2: {q}, 3: {p}}
kat.texvisu("0 \ 2 / 1 > 3", "3 lb 3")
for f in [
q,
(EX, p),
(AX, p),
(EG, p),
(AG, p),
(EF, (EG, p)),
(EF, (AG, p)),
(AF, (EG, p)),
(AF, (AG, p)),
(AU, p, q),
(EU, p, q),
(EU, p, (AND, (NOT, p), (AU, (NOT, p), q))),
(AX, (AX, q)),
(EX, (AX, q)),
(AX, (EX, q)),
(EX, (EX, q)),
(AX, (AF, (AND, p, q))),
(AF, (AX, (AND, p, q))),
]:
checkvisu(kat, labels, f, visu=("simple", "detailed"))
NFA.VISULANG = n
NFA.visutext("Simplify Expressions (Exercise)")
a, b, eps = E("a"), E("b"), E("")
mystery = ( eps | a.star()+(b+a.star()).star()+b )+a.star()
mystery.show()
mystery2 = ( eps | a.star()+( eps | b+(a.star()+b).star()+a.star() )+b )+a.star()
mystery2.show()
ba_BA = (E("aa") | E("bb") |
( (E("ab") | E("ba")) + (E("aa") | E("bb")).star() + (E("ab") | E("ba")) )).star()
ba_BA.show()
NFA.spec("""
AB
AB
AB a aB b Ab
aB a AB b ab
ab a Ab b aB
Ab a ab b AB
""").named("even numbers of a and b").visu()
NFA.visutext("Rational Identities (Exercise)")
α, β = E("α"), E("β")
ident_11 = (α|β).star().show()
ident_12 = (α.star() | β.star()).show()
NFA.VISULANG=6
ident_21 = ( (α+β).star() + α ).show()
ident_22 = ( α+(β+α).star() ).show()
