This DFA accepts a certain language L. In this problem we shall consider certain other languages that are defined by their tails, that is, languages of the form (0+1)*w, for some particular string w of 0's and 1's. Call this language L(w). Depending on w, L(w) may be contained in L, disjoint from L, or neither contained nor disjoint from L (i.e., some strings of the form xw are in L and others are not).
Your problem is to find a way to classify w into one of these three cases. Then, use your knowledge to classify the following languages:
- L(1111001), i.e., the language of regular expression (0+1)*1111001.
- L(11011), i.e., the language of regular expression (0+1)*11011.
- L(110101), i.e., the language of regular expression (0+1)*110101.
- L(00011101), i.e., the language of regular expression (0+1)*00011101.
These are the options:
A). L(1111001) is disjoint from L.
B). L(110101) is contained in L.
C). L(1111001) is contained in L.
D). L(110101) is disjoint from L.