Scikit LogisticRegression cannot learn or,and boolean functions

Question

It seems the LogisticRegression implemented in scikit-learn cannot learn the simple boolean functions AND or OR. I would understand XOR giving bad results but AND and OR should be fine. Am I doing something wrong?

from sklearn.linear_model import LogisticRegression, LinearRegression
import numpy as np

bool_and = np.array([0., 0., 0., 1.])
bool_or  = np.array([0., 1., 1., 1.])
bool_xor = np.array([0., 1., 1., 0.])


x = np.array([[0., 0.],
              [0., 1.],
              [1., 0.],
              [1., 1.]])

y = bool_and
logit = LogisticRegression()
logit.fit(x,y)

#linear = LinearRegression()
#linear.fit(x, y)

print "expected: ", y
print "predicted:", logit.predict(x)
#print linear.predict(x)

gives the following output:

expected:  [0 0 0 1]
predicted: [0 0 0 0]

Answer 1

The problem seems to have to do with regularization. The following makes the classifier work:

logit = LogisticRegression(C=100)

Unfortunately, the documentation is a bit sparse, so I am not sure what the range of the C parameter is.