The question is to design a DFA that accepts a language in which the count of  substring $110$ is no less than the count of substring $011$. For example, $110$, 0101, 0111101110 is good but 011011 is bad.The restriction of the language equivalently means whenever a 011 is encountered, only this pattern $0111^*0$ is allowed, so that a $011$ is matched with a $110$. There is no other restriction.I tried to give a regular expression as $(1^*0111^*0)^* + 1^*0^*$, but I tried very hard but failed to convert this to a DFA. Is there a systematic way to convert such a regular expression to a DFA?
Design the regular expression and DFA that accepts a language in which 110 is no less than 011
automata;finite automata;regular expressions