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)