def generate(data):
data["params"]["hints"] = []
data["params"]["language_description"] = \
"All binary strings such that every prefix $x$ satisfies $|\#_0(x) - \#_1(x)| \le 2$."
server_base.generate(data)
def generate(data):
data["params"]["hints"] = []
data["params"]["language_description"] = \
"All binary strings containing 010 where the total number of 0s is divisible by 3."
server_base.generate(data)
def generate(data):
data["params"]["hints"] = []
data["params"]["language_description"] = \
"All binary strings containing 010 or containing at least three 1s."
server_base.generate(data)
def generate(data):
data["params"]["hints"] = []
data["params"]["language_description"] = \
"All binary strings not containing the substring 000."
server_base.generate(data)
def generate(data):
data["params"]["hints"] = []
data["params"]["language_description"] = \
"All binary strings in which the number of 0s is 2 mod 3."
server_base.generate(data)
def generate(data):
data["params"]["hints"] = []
data["params"]["language_description"] = \
"All binary strings in which every run of 0s has length at least 3."
server_base.generate(data)
def generate(data):
data["params"]["hints"] = []
data["params"]["language_description"] = \
"All binary strings in which 1 does not appear after a substring 000."
server_base.generate(data)
def generate(data):
data["params"]["hints"] = []
data["params"]["language_description"] = \
"All binary strings containing at least two 0s and at least one 1."
server_base.generate(data)
def generate(data):
data["params"]["hints"] = []
data["params"]["language_description"] = \
"The binary representations of all nonnegative integers divisible by 17. " \
"(Leading 0s are allowed, and an empty string should be interpreted as 0.)"
server_base.generate(data)
def generate(data):
data["params"]["hints"] = [
"Create a DFA that accepts strings containing 010. "
"Then, take the complement of that DFA."
]
data["params"]["language_description"] = \
"All binary strings not containing the substring 010."
server_base.generate(data)
def generate(data):
data["params"]["hints"] = [
"For what values of $n$ does the substring $000$ appear in $0^n$ an odd number of times?",
"Consider the maximal blocks of 0s that appear in a string. For example, in $10001101110000100000$, "
"the maximal blocks of 0s are $$1(000)11(0)111(0000)1(00000).$$"
"Then, consider the number of occurrences of $000$ contributed by each block.",
"Some of these blocks contribute an odd number of occurrences of $000$. We want those "
"types of blocks to appear an even number of times."
]
data["params"]["language_description"] = \
"All binary strings in which the substring $000$ appears an even number of times."
server_base.generate(data)