Commit 2d8d8186 authored by Niklas Rieken's avatar Niklas Rieken
Browse files

abstracted pumping lemma game in python

parent cda3f3d5
import sys
import random
# configuration
lang = "{a^n b^n : n in IN}" # language
maxn = 10 # maximal number of states
# checks if a word w is in the language L
def L(w):
i = 0
mid = False
for a in w:
if a not in ['a', 'b']:
return False
if a == 'a' and not mid:
i += 1
if a == 'a' and mid:
return False
if a == 'b' and mid:
i -= 1
if a == 'b' and not mid:
mid = True
i -= 1
return (i == 0)
# choose a number of states
def choose_n(minn=1, maxn=maxn):
return random.randint(minn, maxn)
# checks if a word is long enough
def length(w, m):
return (len(w) >= m)
# decomposition strategy
def decompose(n, w):
k = random.randint(0, n-1)
l = random.randint(k+1, n)
return k, l
# play
# 1. Alice chooses number of states n
n = choose_n()
print("Alice claims the language {0} is regular and there exists an automaton with {1} states.".format(lang, n))
# 2. Bob chooses word w
w = input("Choose a word in the language of length >= {0}: ".format(n))
if not L(w):
sys.exit("Your word is not in the language. You lose.")
elif not length(w, n):
sys.exit("Your word is too short. You loose.")
# 3. Alice chooses decomposition xyz
k, l = decompose(n, w)
x = w[:k]
y = w[k:l]
z = w[l:]
print("Alice chooses the decomposition x = {0}, y = {1}, z = {2}.".format(x, y, z))
# 4. Bob chooses pumping number i
i = int(input("Choose a natural number i sucht that w' = xy^iz is not in the language: "))
wp = x + y*i + z
if not L(wp):
print("w' = xy^{0}z is not in the language. You win.".format(i))
sys.exit("w' = xy^{0}z is in the language. You lose.".format(i))
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